In the recovery-based estimates method, we employ a projection technique to recover a post-proces... more In the recovery-based estimates method, we employ a projection technique to recover a post-processed quantity (usually the stresses or the gradient computed from the FE-approximation). The error is estimated by taking the difference between the recovered quantity and the FE-solution. An easy procedure to implement is the continuous global L2 (CGL2) recovery initially used for a posteriori error estimation by Zienkiewicz and Zhu [1]. Kumar, Kvamsdal and Johannessen [2] developed CGL2 and Superconvergent Patch Recovery (SPR) error estimation methods applicable for adaptive refinement using LR B-splines [3] and observed very good results for both the CGL2 and the SPR recovery technique. However, Cai and Zhang reported in [4] a case of malfunction for the CGL2recovery applied to second order triangular and tetrahedral Lagrange finite element. Here we will start out by presenting a motivational example that illustrates the benefits of using high regularity splines in the CGL2 based gradient recovery procedure compared to using the classical Lagrange FEM basis functions. We will then show the performance on some benchmark problems comparing the use of splines versus Lagrange basis functions.
Pressure oscillations at small time steps have been known to be an issue in poroelasticity simula... more Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite element analyses. We present a mixed isogeometric formulation here with a view to assessing the results at very small time steps. Numerical studies are performed on Terzaghi’s problem and consolidation of a layered porous medium with a very low permeability layer for varying polynomial degrees, continuities across knot spans and spatial discretizations. Comparisons are made with equal order simulations.
This time we gather in Tønsberg, the centre of a popular summer resort area and Norway's oldest c... more This time we gather in Tønsberg, the centre of a popular summer resort area and Norway's oldest city, dating back to early Viking times. This conference series is integrated with the French conferences (Curves and Surfaces) organised by SMAI-Association Francaise d'Approximation, and the next conference will be in Avignon, France in 2010. With more than 170 participants and almost 140 talks, including 9 invited speakers and 7 minisymposia, the week is going to be very busy, with a varied and interesting scientific program. We have attempted to group related talks together, but please note that there has been some late rescheduling that may have caused seemingly unrelated talks to end up together. The conference proceedings will be published in an international journal. Details about submission of manuscripts will be announced during the conference, and on www.ifi.uio.no/˜cagd/ after the conference. As usual, we have had considerable help from a number of people. Andrew McMurry has helped with web programming, scripts and other technical challenges. Anne Cathrine and Nina Modahl have provided expert help with all financial issues, and Sara Mørken will assist us with registration in Tønsberg. Thank you very much to all of you! We are grateful for financial support from the Department of Informatics and the Centre of Mathematics for Applications at the University of Oslo, and from the eVITA Program in the Research Council of Norway Last, but not least, we thank you, the participants, for your contributions-without you, there simply would be no conference.
It is well-known that smooth tensor product splines, such as NURBS, are inherently weak in captur... more It is well-known that smooth tensor product splines, such as NURBS, are inherently weak in capturing rapidly varying fields and sharp local gradients. Hence, in isogeometric analysis (IGA), they perform poorly in the presence of thin layers or singularities. The prevailing idea for addressing these types of problems, which has recently been extensively explored, is providing the adaptive local refinement property by employing hierarchical splines [1,2]. In this paper, we introduce a novel adaptive w-refinement technique in isogeometric analysis based on a proposed generalization of NURBS, referred to as generalized NURBS (GNURBS), as an alternative fundamental approach for dealing with the aforementioned problems. This generalization is obtained by decoupling of the weights associated with the basis functions in geometry and field variable space. Considering the additional unknown control weights in the function space as design variables, we subsequently develop two different adapti...
Pressure oscillations at small time steps have been known to be an issue in poroelasticity simula... more Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite element analyses. We present a mixed isogeometric formulation here with a view to assessing the results at very small time steps. Numerical studies are performed on Terzaghi's problem and consolidation of a layered porous medium with a very low permeability layer for varying polynomial degrees, continuities across knot spans and spatial discretizations. Comparisons are made with equal order simulations.
District heating networks are commonly addressed in the literature as one of the most effective s... more District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand-outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.
We present a nonintrusive approach for combining high-fidelity simulations using Finite-Volume (F... more We present a nonintrusive approach for combining high-fidelity simulations using Finite-Volume (FV) methods with Proper Orthogonal Decomposition (POD) and Galerkin Reduced-Order Modeling (ROM) methodology. By nonintrusive we here imply an approach that does not need specific knowledge about the high-fidelity Computational Fluid Dynamics (CFD) solver other than the velocity and pressure results given on an element mesh representing the related discrete interpolation spaces. The key step in the presented approach is the projection of the FV results onto suitable finite-element (FE) spaces and then use of classical POD Galerkin ROM framework. We do a numerical investigation of aerodynamic flow around an airfoil cross-section (NACA64) at low Reynolds number and compare the ROM results obtained with high-fidelity FV-generated snapshots against similar high-fidelity results obtained with FE using Taylor–Hood velocity and pressure spaces. Our results show that we achieve relative errors in...
District heating networks are commonly addressed in the literature as one of the most effective s... more District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand-outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.
The key to the better design of an industrial scale wind turbine is to understand the influence o... more The key to the better design of an industrial scale wind turbine is to understand the influence of blade geometry and its dynamics on the complicated flow-structures. An industrial-scale wind turbine can be numerically represented using various approaches (from simpler 2D steady flow to complex 3D with moving mesh, with and without the inclusion of hubs) that can alter the results substantially. At the same time, to standardize and test methodologies, the reference industrial-scale NREL 5 MW wind turbine is gaining popularity. The wind energy community will learn through an improved understanding of the aerodynamics of this NREL 5 MW reference mega−watt size wind turbine by taking into consideration the various levels of geometric approximations. Hence, in this work the NREL 5MW reference wind turbine is used for both: (a) understanding the associated flow-complexities due to various geometric approximation, and (b) comparison and validation of the performance of different numerical approaches for flow-simulation. The various geometric approximations considered here are related to simulating the influence of the shape of turbines structure (blade, an inclusion of hub, tower) and motions of blades. It involves (a) influence of 2D, 2.5D and 3D turbine blade geometry to highlight the impact of section bluntness, (b) influence of steady frozen rotor and rotating rotor simulations and (c) influence of inclusion of hub through a full-scale geometry of the complete reference turbine. Furthermore, the key features of the flow dynamics of a rotor and full machine are identified and parametric studies are conducted to evaluate overall performance prediction under variable Tip Speed Ratios
Prevailing atmospheric conditions can have a significant impact on the performance of large megaw... more Prevailing atmospheric conditions can have a significant impact on the performance of large megawatt wind turbines. A purely experimental evaluation of this impact is currently not possible and hence numerical techniques have been employed in this work. With the focus on aerodynamic performance of wind turbine, an attempt is made to realize the following objectives: (a) To evaluate the predictive capabilities of fully resolved Sliding Mesh Interface (SMI) transient simulations around the wind turbine against the steady state Multiple Reference Frame (MRF) simulations (b) To investigate the performance of the wind turbine subjected to uniform inlet profiles against atmospheric boundary layer profiles. (c) To study the effect of atmospheric stability on wind turbine performance. The methods are validated first and then implemented on a national renewable energy laboratory 5 MW reference wind turbine model for the aerodynamic study. Highly uneven and irregular wake profiles are seen with variation in input conditions(TKE). Uneven distribution of flow velocity in the lateral direction enhances the momentum transfer with in the shear layers and contributes positively towards the wake recovery. It is also found that in unstable stratified conditions, the positive buoyancy flux at the surface creates thermal instabilities which enhances the turbulent kinetic energy and the turbulent mixing, and helps the wake to recover faster.
Defining wake characteristics from scanning and vertical full-scale lidar measurements R J Barthe... more Defining wake characteristics from scanning and vertical full-scale lidar measurements R J Barthelmie, P Doubrawa, H Wang et al. Lattice Boltzmann Simulation of the Cross Flow Over a Cantilevered and Longitudinally Vibrating Circular Cylinder Xia Yong, Lu De-Tang, Liu Yang et al. Aspects of the influence of an oscillating mini-flap upon the near wake of an airfoil NACA 4412
Offshore wind energy is one of the most competitive renewable energy resources available to us, w... more Offshore wind energy is one of the most competitive renewable energy resources available to us, which until now been underexploited. Most of the problems associated with wind farm installation like land acquisition, low wind conditions and its visual impact can be eliminated to large extent by going offshore. In fact it is expected that by the year 2020, 40GW of offshore wind power capacity will be in operation. In an offshore context the wind turbine design methodologies have to address new challenges. For optimal performance the turbine needs to be huge in size and for horizontal axis wind turbines (HAWT) the diameter has already reached a size of 200m. Till now little attention has been paid to vertical axis offshore wind turbines. However, within the NOWITECH project new concepts for vertical axis turbine have been proposed and it might not take a long time before such turbines may become an realistic alternative for use offshore. The current work characterizes variable turbulence intensity flow field around a rotating vertical axis wind turbine (VAWT) in an offshore context. Complete three dimensional numerical transient simulations are performed accounting for the variation of multiple turbulence intensity levels associated with the oncoming wind. Usually offshore winds are highly turbulent in nature partially because of the rapid changes in wind directions along with the sea-air interaction. The results from the study indicate that due to the increase in the turbulence intensity level of 5% to 25% the performance of wind turbine decreases by almost 23% to 42% compared to no turbulence in the incoming wind field.
Computer Methods in Applied Mechanics and Engineering, 2015
To solve the incompressible flow problems using isogeometric analysis, the div-compatible spline ... more To solve the incompressible flow problems using isogeometric analysis, the div-compatible spline spaces were originally introduced by Buffa [10, 11], and later developed by Evans [20]. In this paper, we extend the div-compatible spline spaces with local refinement capability using Locally Refined (LR) B-splines over rectangular domains. We argue that the spline spaces generated on locally refined meshes will satisfy compatibility provided they span the entire function spaces as governed by Mourrains [29] dimension formula. We will in this work use the structured refined LR B-splines as introduced by Johannessen et al. [25]. Further, we consider these div-compatible LR B-spline spaces to approximate the velocity and pressure fields in mixed discretization for Stokes problem and a set of standard benchmark tests are performed to show the stability, efficiency and the conservation properties of the discrete velocity fields in adaptive isogeometric analysis.
Computer Methods in Applied Mechanics and Engineering, 2015
Smooth spline functions such as B-splines and NURBS are already an established technology in the ... more Smooth spline functions such as B-splines and NURBS are already an established technology in the field of computer-aided design (CAD) and have in recent years been given a lot of attention from the computer-aided engineering (CAE) community. The advantages of local refinement are obvious for anyone working in either field, and as such, several approaches have been proposed. Among others, we find the three strategies Classical Hierarchical B-splines, Truncated Hierarchical B-splines and Locally Refined B-splines. We will in this paper present these three frameworks and highlight similarities and differences between them. In particular, we will look at the function space they span and the support of the basis functions. We will then analyse the corresponding stiffness and mass matrices in terms of sparsity patterns and conditioning numbers. We show that the basis in general do not span the same space, and that conditioning numbers are comparable. Moreover we show that the weighting needed by the Classical Hierarchical basis to maintain partition of unity has significant implications on the conditioning numbers.
Computer Methods in Applied Mechanics and Engineering, 2015
Implementation of three different Navier-Stokes solvers in an isogeometric finite element framewo... more Implementation of three different Navier-Stokes solvers in an isogeometric finite element framework is presented in this paper. The three solvers Chorin projection method and Coupled formulation, both with the Spalart-Allmaras turbulence model, and Variational Multiscale (VMS) method have been applied to simulate flow past a two-dimensional NACA0012 airfoil at a high Reynolds number (Re = 3 × 10 6) for four different angles of attack. The predicted flow characteristics have been compared and the effects of increasing the order of the spline element on the accuracy of prediction and computational efficiency is evaluated. In this study it turns out that flow separation does not take place up to an angle of attack of 16 •. Up to this angle of attack all three solvers predict similar results in good agreement with each other and with available experimental results. However, a big spread in lift and drag coefficients is observed in the stall regime. Our study also shows that for linear spline elements all three solvers are computationally similar. For quadratic spline elements the Chorin solver compares favorably to the others based on the results presented here.
Computer Methods in Applied Mechanics and Engineering, 2014
The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al. [6] may h... more The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al. [6] may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis. In this paper, we propose local refinement strategies for adaptive isogeometric analysis using LR B-splines and investigate its performance by doing numerical tests on well known benchmark cases. The theory behind LR B-spline is not presented in full details, but the main conceptual ingredients are explained and illustrated by a number of examples.
Most mesoscale models are developed with grid resolution in the range of kilometers. Therefore, t... more Most mesoscale models are developed with grid resolution in the range of kilometers. Therefore, they may require spatial averaging to analyze flow behavior over the domain of interest. In doing so, certain important features of sub-grid scales are lost. Moreover, spatial averaging on the governing equations results in additional terms known as dispersive fluxes. These fluxes are ignored in the analysis. The aim of this paper is to identify the significance of these fluxes for accurate assessment of flow fields related to wind farm applications. The research objectives are hence twofold: 1) to quantify the impact of wind turbines on MBL characteristics. 2) to account for the magnitude of dispersive fluxes arising from spatial averaging and make a comparison against the turbulent flux values. To conduct the numerical study the NREL 5MW reference wind turbine model is employed with a RANS approach using k-ε turbulence model. The results are presented concerning spatially averaged veloc...
The problem at hand is a coupled acoustic-structure interaction (ASI) on an unbounded domain. An ... more The problem at hand is a coupled acoustic-structure interaction (ASI) on an unbounded domain. An object of elastic material is surrounded by fluid. Using physical assumptions, the fluid is described by the wave equation, which is transformed to the Helmholtz equation. That is, we consider the frequency domain instead of the time domain. Both the infinite element method (IEM) [1] and the boundary element method (BEM) have been investigated on the acoustic scattering problem using the isogeometric method [2]. As the computer aided design (CAD) files typically parameterizes the boundary of the scatterer, the IGABEM represents the ideal bridge between design and analysis. The BEM method result in a dense matrix, which is computationally expensive to build. The infinite element method resolves this issue, but introduces a volume domain to be discretised, which weakens the bridge between CAD and IGA. When combining IGA with these methods we again observe significant improvements over clas...
Isogeometric analysis [1] (IGA) of acoustic scattering on unbounded domains has, as in many other... more Isogeometric analysis [1] (IGA) of acoustic scattering on unbounded domains has, as in many other fields, shown promising results. In [2] we obtained very good results using isogeometric infinite elements both for solving scattering of rigid spheres and acoustic-structure interaction problems. We verified numerically toward the exact solution given in [3] that IGA using full regularity splines (Cp−1) of order p, achieved significantly less errors than classical infinite elements using C0-Lagrange polynomials of same polynomial order. However, methods that introduce an artificial boundary (infinite element method, PML-method, ABC-operators etc.) to handle the unbounded domain introduce the problem of surfaceto-volume parametrization between the scatterer and the artificial boundary, reducing the quality of the bridge between design and analysis provided by IGA. As the boundary element method (BEM) avoids this problem in only requiring a parameterization of the scatterer, it represent...
A digital twin can be defined as an adaptive model of a complex physical system. Recent advances ... more A digital twin can be defined as an adaptive model of a complex physical system. Recent advances in computational pipelines, multiphysics solvers, artificial intelligence, big data cybernetics, data processing and management tools bring the promise of digital twins and their impact on society closer to reality. Digital twinning is now an important and emerging trend in many applications. Also referred to as a computational megamodel, device shadow, mirrored system, avatar or a synchronized virtual prototype, there can be no doubt that a digital twin plays a transformative role not only in how we design and operate cyber-physical intelligent systems, but also in how we advance the modularity of multi-disciplinary systems to tackle fundamental barriers not addressed by the current, evolutionary modeling practices. In this work, we review the recent status of methodologies and techniques related to the construction of digital twins. Our aim is to provide a detailed coverage of the curr...
In the recovery-based estimates method, we employ a projection technique to recover a post-proces... more In the recovery-based estimates method, we employ a projection technique to recover a post-processed quantity (usually the stresses or the gradient computed from the FE-approximation). The error is estimated by taking the difference between the recovered quantity and the FE-solution. An easy procedure to implement is the continuous global L2 (CGL2) recovery initially used for a posteriori error estimation by Zienkiewicz and Zhu [1]. Kumar, Kvamsdal and Johannessen [2] developed CGL2 and Superconvergent Patch Recovery (SPR) error estimation methods applicable for adaptive refinement using LR B-splines [3] and observed very good results for both the CGL2 and the SPR recovery technique. However, Cai and Zhang reported in [4] a case of malfunction for the CGL2recovery applied to second order triangular and tetrahedral Lagrange finite element. Here we will start out by presenting a motivational example that illustrates the benefits of using high regularity splines in the CGL2 based gradient recovery procedure compared to using the classical Lagrange FEM basis functions. We will then show the performance on some benchmark problems comparing the use of splines versus Lagrange basis functions.
Pressure oscillations at small time steps have been known to be an issue in poroelasticity simula... more Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite element analyses. We present a mixed isogeometric formulation here with a view to assessing the results at very small time steps. Numerical studies are performed on Terzaghi’s problem and consolidation of a layered porous medium with a very low permeability layer for varying polynomial degrees, continuities across knot spans and spatial discretizations. Comparisons are made with equal order simulations.
This time we gather in Tønsberg, the centre of a popular summer resort area and Norway's oldest c... more This time we gather in Tønsberg, the centre of a popular summer resort area and Norway's oldest city, dating back to early Viking times. This conference series is integrated with the French conferences (Curves and Surfaces) organised by SMAI-Association Francaise d'Approximation, and the next conference will be in Avignon, France in 2010. With more than 170 participants and almost 140 talks, including 9 invited speakers and 7 minisymposia, the week is going to be very busy, with a varied and interesting scientific program. We have attempted to group related talks together, but please note that there has been some late rescheduling that may have caused seemingly unrelated talks to end up together. The conference proceedings will be published in an international journal. Details about submission of manuscripts will be announced during the conference, and on www.ifi.uio.no/˜cagd/ after the conference. As usual, we have had considerable help from a number of people. Andrew McMurry has helped with web programming, scripts and other technical challenges. Anne Cathrine and Nina Modahl have provided expert help with all financial issues, and Sara Mørken will assist us with registration in Tønsberg. Thank you very much to all of you! We are grateful for financial support from the Department of Informatics and the Centre of Mathematics for Applications at the University of Oslo, and from the eVITA Program in the Research Council of Norway Last, but not least, we thank you, the participants, for your contributions-without you, there simply would be no conference.
It is well-known that smooth tensor product splines, such as NURBS, are inherently weak in captur... more It is well-known that smooth tensor product splines, such as NURBS, are inherently weak in capturing rapidly varying fields and sharp local gradients. Hence, in isogeometric analysis (IGA), they perform poorly in the presence of thin layers or singularities. The prevailing idea for addressing these types of problems, which has recently been extensively explored, is providing the adaptive local refinement property by employing hierarchical splines [1,2]. In this paper, we introduce a novel adaptive w-refinement technique in isogeometric analysis based on a proposed generalization of NURBS, referred to as generalized NURBS (GNURBS), as an alternative fundamental approach for dealing with the aforementioned problems. This generalization is obtained by decoupling of the weights associated with the basis functions in geometry and field variable space. Considering the additional unknown control weights in the function space as design variables, we subsequently develop two different adapti...
Pressure oscillations at small time steps have been known to be an issue in poroelasticity simula... more Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite element analyses. We present a mixed isogeometric formulation here with a view to assessing the results at very small time steps. Numerical studies are performed on Terzaghi's problem and consolidation of a layered porous medium with a very low permeability layer for varying polynomial degrees, continuities across knot spans and spatial discretizations. Comparisons are made with equal order simulations.
District heating networks are commonly addressed in the literature as one of the most effective s... more District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand-outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.
We present a nonintrusive approach for combining high-fidelity simulations using Finite-Volume (F... more We present a nonintrusive approach for combining high-fidelity simulations using Finite-Volume (FV) methods with Proper Orthogonal Decomposition (POD) and Galerkin Reduced-Order Modeling (ROM) methodology. By nonintrusive we here imply an approach that does not need specific knowledge about the high-fidelity Computational Fluid Dynamics (CFD) solver other than the velocity and pressure results given on an element mesh representing the related discrete interpolation spaces. The key step in the presented approach is the projection of the FV results onto suitable finite-element (FE) spaces and then use of classical POD Galerkin ROM framework. We do a numerical investigation of aerodynamic flow around an airfoil cross-section (NACA64) at low Reynolds number and compare the ROM results obtained with high-fidelity FV-generated snapshots against similar high-fidelity results obtained with FE using Taylor–Hood velocity and pressure spaces. Our results show that we achieve relative errors in...
District heating networks are commonly addressed in the literature as one of the most effective s... more District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand-outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.
The key to the better design of an industrial scale wind turbine is to understand the influence o... more The key to the better design of an industrial scale wind turbine is to understand the influence of blade geometry and its dynamics on the complicated flow-structures. An industrial-scale wind turbine can be numerically represented using various approaches (from simpler 2D steady flow to complex 3D with moving mesh, with and without the inclusion of hubs) that can alter the results substantially. At the same time, to standardize and test methodologies, the reference industrial-scale NREL 5 MW wind turbine is gaining popularity. The wind energy community will learn through an improved understanding of the aerodynamics of this NREL 5 MW reference mega−watt size wind turbine by taking into consideration the various levels of geometric approximations. Hence, in this work the NREL 5MW reference wind turbine is used for both: (a) understanding the associated flow-complexities due to various geometric approximation, and (b) comparison and validation of the performance of different numerical approaches for flow-simulation. The various geometric approximations considered here are related to simulating the influence of the shape of turbines structure (blade, an inclusion of hub, tower) and motions of blades. It involves (a) influence of 2D, 2.5D and 3D turbine blade geometry to highlight the impact of section bluntness, (b) influence of steady frozen rotor and rotating rotor simulations and (c) influence of inclusion of hub through a full-scale geometry of the complete reference turbine. Furthermore, the key features of the flow dynamics of a rotor and full machine are identified and parametric studies are conducted to evaluate overall performance prediction under variable Tip Speed Ratios
Prevailing atmospheric conditions can have a significant impact on the performance of large megaw... more Prevailing atmospheric conditions can have a significant impact on the performance of large megawatt wind turbines. A purely experimental evaluation of this impact is currently not possible and hence numerical techniques have been employed in this work. With the focus on aerodynamic performance of wind turbine, an attempt is made to realize the following objectives: (a) To evaluate the predictive capabilities of fully resolved Sliding Mesh Interface (SMI) transient simulations around the wind turbine against the steady state Multiple Reference Frame (MRF) simulations (b) To investigate the performance of the wind turbine subjected to uniform inlet profiles against atmospheric boundary layer profiles. (c) To study the effect of atmospheric stability on wind turbine performance. The methods are validated first and then implemented on a national renewable energy laboratory 5 MW reference wind turbine model for the aerodynamic study. Highly uneven and irregular wake profiles are seen with variation in input conditions(TKE). Uneven distribution of flow velocity in the lateral direction enhances the momentum transfer with in the shear layers and contributes positively towards the wake recovery. It is also found that in unstable stratified conditions, the positive buoyancy flux at the surface creates thermal instabilities which enhances the turbulent kinetic energy and the turbulent mixing, and helps the wake to recover faster.
Defining wake characteristics from scanning and vertical full-scale lidar measurements R J Barthe... more Defining wake characteristics from scanning and vertical full-scale lidar measurements R J Barthelmie, P Doubrawa, H Wang et al. Lattice Boltzmann Simulation of the Cross Flow Over a Cantilevered and Longitudinally Vibrating Circular Cylinder Xia Yong, Lu De-Tang, Liu Yang et al. Aspects of the influence of an oscillating mini-flap upon the near wake of an airfoil NACA 4412
Offshore wind energy is one of the most competitive renewable energy resources available to us, w... more Offshore wind energy is one of the most competitive renewable energy resources available to us, which until now been underexploited. Most of the problems associated with wind farm installation like land acquisition, low wind conditions and its visual impact can be eliminated to large extent by going offshore. In fact it is expected that by the year 2020, 40GW of offshore wind power capacity will be in operation. In an offshore context the wind turbine design methodologies have to address new challenges. For optimal performance the turbine needs to be huge in size and for horizontal axis wind turbines (HAWT) the diameter has already reached a size of 200m. Till now little attention has been paid to vertical axis offshore wind turbines. However, within the NOWITECH project new concepts for vertical axis turbine have been proposed and it might not take a long time before such turbines may become an realistic alternative for use offshore. The current work characterizes variable turbulence intensity flow field around a rotating vertical axis wind turbine (VAWT) in an offshore context. Complete three dimensional numerical transient simulations are performed accounting for the variation of multiple turbulence intensity levels associated with the oncoming wind. Usually offshore winds are highly turbulent in nature partially because of the rapid changes in wind directions along with the sea-air interaction. The results from the study indicate that due to the increase in the turbulence intensity level of 5% to 25% the performance of wind turbine decreases by almost 23% to 42% compared to no turbulence in the incoming wind field.
Computer Methods in Applied Mechanics and Engineering, 2015
To solve the incompressible flow problems using isogeometric analysis, the div-compatible spline ... more To solve the incompressible flow problems using isogeometric analysis, the div-compatible spline spaces were originally introduced by Buffa [10, 11], and later developed by Evans [20]. In this paper, we extend the div-compatible spline spaces with local refinement capability using Locally Refined (LR) B-splines over rectangular domains. We argue that the spline spaces generated on locally refined meshes will satisfy compatibility provided they span the entire function spaces as governed by Mourrains [29] dimension formula. We will in this work use the structured refined LR B-splines as introduced by Johannessen et al. [25]. Further, we consider these div-compatible LR B-spline spaces to approximate the velocity and pressure fields in mixed discretization for Stokes problem and a set of standard benchmark tests are performed to show the stability, efficiency and the conservation properties of the discrete velocity fields in adaptive isogeometric analysis.
Computer Methods in Applied Mechanics and Engineering, 2015
Smooth spline functions such as B-splines and NURBS are already an established technology in the ... more Smooth spline functions such as B-splines and NURBS are already an established technology in the field of computer-aided design (CAD) and have in recent years been given a lot of attention from the computer-aided engineering (CAE) community. The advantages of local refinement are obvious for anyone working in either field, and as such, several approaches have been proposed. Among others, we find the three strategies Classical Hierarchical B-splines, Truncated Hierarchical B-splines and Locally Refined B-splines. We will in this paper present these three frameworks and highlight similarities and differences between them. In particular, we will look at the function space they span and the support of the basis functions. We will then analyse the corresponding stiffness and mass matrices in terms of sparsity patterns and conditioning numbers. We show that the basis in general do not span the same space, and that conditioning numbers are comparable. Moreover we show that the weighting needed by the Classical Hierarchical basis to maintain partition of unity has significant implications on the conditioning numbers.
Computer Methods in Applied Mechanics and Engineering, 2015
Implementation of three different Navier-Stokes solvers in an isogeometric finite element framewo... more Implementation of three different Navier-Stokes solvers in an isogeometric finite element framework is presented in this paper. The three solvers Chorin projection method and Coupled formulation, both with the Spalart-Allmaras turbulence model, and Variational Multiscale (VMS) method have been applied to simulate flow past a two-dimensional NACA0012 airfoil at a high Reynolds number (Re = 3 × 10 6) for four different angles of attack. The predicted flow characteristics have been compared and the effects of increasing the order of the spline element on the accuracy of prediction and computational efficiency is evaluated. In this study it turns out that flow separation does not take place up to an angle of attack of 16 •. Up to this angle of attack all three solvers predict similar results in good agreement with each other and with available experimental results. However, a big spread in lift and drag coefficients is observed in the stall regime. Our study also shows that for linear spline elements all three solvers are computationally similar. For quadratic spline elements the Chorin solver compares favorably to the others based on the results presented here.
Computer Methods in Applied Mechanics and Engineering, 2014
The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al. [6] may h... more The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al. [6] may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis. In this paper, we propose local refinement strategies for adaptive isogeometric analysis using LR B-splines and investigate its performance by doing numerical tests on well known benchmark cases. The theory behind LR B-spline is not presented in full details, but the main conceptual ingredients are explained and illustrated by a number of examples.
Most mesoscale models are developed with grid resolution in the range of kilometers. Therefore, t... more Most mesoscale models are developed with grid resolution in the range of kilometers. Therefore, they may require spatial averaging to analyze flow behavior over the domain of interest. In doing so, certain important features of sub-grid scales are lost. Moreover, spatial averaging on the governing equations results in additional terms known as dispersive fluxes. These fluxes are ignored in the analysis. The aim of this paper is to identify the significance of these fluxes for accurate assessment of flow fields related to wind farm applications. The research objectives are hence twofold: 1) to quantify the impact of wind turbines on MBL characteristics. 2) to account for the magnitude of dispersive fluxes arising from spatial averaging and make a comparison against the turbulent flux values. To conduct the numerical study the NREL 5MW reference wind turbine model is employed with a RANS approach using k-ε turbulence model. The results are presented concerning spatially averaged veloc...
The problem at hand is a coupled acoustic-structure interaction (ASI) on an unbounded domain. An ... more The problem at hand is a coupled acoustic-structure interaction (ASI) on an unbounded domain. An object of elastic material is surrounded by fluid. Using physical assumptions, the fluid is described by the wave equation, which is transformed to the Helmholtz equation. That is, we consider the frequency domain instead of the time domain. Both the infinite element method (IEM) [1] and the boundary element method (BEM) have been investigated on the acoustic scattering problem using the isogeometric method [2]. As the computer aided design (CAD) files typically parameterizes the boundary of the scatterer, the IGABEM represents the ideal bridge between design and analysis. The BEM method result in a dense matrix, which is computationally expensive to build. The infinite element method resolves this issue, but introduces a volume domain to be discretised, which weakens the bridge between CAD and IGA. When combining IGA with these methods we again observe significant improvements over clas...
Isogeometric analysis [1] (IGA) of acoustic scattering on unbounded domains has, as in many other... more Isogeometric analysis [1] (IGA) of acoustic scattering on unbounded domains has, as in many other fields, shown promising results. In [2] we obtained very good results using isogeometric infinite elements both for solving scattering of rigid spheres and acoustic-structure interaction problems. We verified numerically toward the exact solution given in [3] that IGA using full regularity splines (Cp−1) of order p, achieved significantly less errors than classical infinite elements using C0-Lagrange polynomials of same polynomial order. However, methods that introduce an artificial boundary (infinite element method, PML-method, ABC-operators etc.) to handle the unbounded domain introduce the problem of surfaceto-volume parametrization between the scatterer and the artificial boundary, reducing the quality of the bridge between design and analysis provided by IGA. As the boundary element method (BEM) avoids this problem in only requiring a parameterization of the scatterer, it represent...
A digital twin can be defined as an adaptive model of a complex physical system. Recent advances ... more A digital twin can be defined as an adaptive model of a complex physical system. Recent advances in computational pipelines, multiphysics solvers, artificial intelligence, big data cybernetics, data processing and management tools bring the promise of digital twins and their impact on society closer to reality. Digital twinning is now an important and emerging trend in many applications. Also referred to as a computational megamodel, device shadow, mirrored system, avatar or a synchronized virtual prototype, there can be no doubt that a digital twin plays a transformative role not only in how we design and operate cyber-physical intelligent systems, but also in how we advance the modularity of multi-disciplinary systems to tackle fundamental barriers not addressed by the current, evolutionary modeling practices. In this work, we review the recent status of methodologies and techniques related to the construction of digital twins. Our aim is to provide a detailed coverage of the curr...
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Papers by Trond Kvamsdal