For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a proble... more For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificialviscosity-based damping into the momentum conservation equation. Then, operator splitting methods are introduced to discretize the added viscous term for relaxing the time-step limit. To further improve the convergence rate, a random-choice strategy is adopted, in which the viscous term is imposed randomly rather than at every time step. In addition, to avoid the thread-conflict induced by applying shared-memory parallelization to accelerate implicit method, a splitting cell-linked list scheme is devised. A number of benchmark tests suggest that the present method helps systems achieve equilibrium state efficiently.
Comparative evaluation lies at the heart of science, and determining the accuracy of a computatio... more Comparative evaluation lies at the heart of science, and determining the accuracy of a computational method is crucial for evaluating its potential as well as for guiding future efforts. However, metrics that are typically used have inherent shortcomings when faced with the under-resolved solutions of realworld simulation problems. We show how to leverage crowd-sourced user studies in order to address the fundamental problems of widely used classical evaluation metrics. We demonstrate that such user studies, which inherently rely on the human visual system, yield a very robust metric and consistent answers for complex phenomena without any requirements for proficiency regarding the physics at hand. This holds even for cases away from convergence where traditional metrics often end up inconclusive results. More specifically, we evaluate results of different essentially non-oscillatory (ENO) schemes in different fluid flow settings. Our methodology represents a novel and practical approach for scientific evaluations that can give answers for previously unsolved problems.
We have developed a multi-phase SPH method to simulate arbitrary interfaces containing surface ac... more We have developed a multi-phase SPH method to simulate arbitrary interfaces containing surface active agents (surfactants) that locally change the properties of the int erface, such the surface tension coefficient [1]. Our method incorpo rates the effects of surface diffusion, transport of surfactant from/to the bulk phase to/from the interface and diffusion in the bulk phase. Neglecting transport mechanisms, we use this method to study the impact of insoluble surfactants on drop deformati on and breakup in simple shear flow.
Computer Methods in Applied Mechanics and Engineering, 2020
In this paper, we propose a consistent parallel unstructured mesh generator based on a multi-phas... more In this paper, we propose a consistent parallel unstructured mesh generator based on a multi-phase SPH method. A set of physics-motivated modeling equations are developed to achieve the targets of domain decomposition, communication volume optimization and high-quality unstructured mesh generation simultaneously. A unified density field is defined as the target function for both partitioning the geometry and distributing the mesh-vertexes. A multi-phase Smoothing Particle Hydrodynamics (SPH) method is employed to solve the governing equations. All the optimization targets are achieved implicitly and consistently by the particle relaxation procedure without constructing triangulation/tetrahedralization explicitly. The target of communication reduction is achieved by introducing a surface tension model between distinct partitioning sub-domains, which are characterized by colored SPH particles. The resulting partitioning diagram features physically localized sub-domains and optimized interface communication. The target of optimiz
In this paper, we extend the method (Fu et al., [1]) to anisotropic meshes by introducing an adap... more In this paper, we extend the method (Fu et al., [1]) to anisotropic meshes by introducing an adaptive SPH (ASPH) concept with ellipsoidal kernels. First, anisotropic target feature-size and density functions, taking into account the effects of singularities, are defined based on the level-set methodology. Second, ASPH is developed such that the particle distribution relaxes towards the target functions. In order to prevent SPH particles from escaping the mesh generation regions, a ghost surface particle method is proposed in combination with a tailored interaction strategy. Necessary adaptations of supporting numerical algorithms, such as fast neighbor search, for enforcing mesh anisotropy are addressed. Finally, unstructured meshes are generated by an anisotropic Delaunay triangulation conforming to the Riemannian metrics for the resulting particle configuration. The performance of the proposed method is demonstrated by a set of benchmark cases.
A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based ... more A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based on spatial filtering by utilizing smoothed particle hydrodynamics (SPH) approximations. This model is similar to our previous developed SPH dis
We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshles... more We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning subdomains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.
29th International Symposium on Shock Waves 2, 2015
In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenome... more In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenomena in simulating high Mach number flow, and the inaccurate pressure profile in simulating low Mach number flow. We introduced two simple low-Mach-number modifications for the classical Roe flux to decrease the difference between the acoustic and advection contributions of the numerical dissipation. While the first modification increases the local numerical dissipation, the second decreases it. The numerical tests on the double-Mach reflection problem show that both modifications eliminate the kinked Mach stem suffered by the original flux. These results suggest that, other than insufficient numerical dissipation near the shock front, the carbuncle phenomena is strongly relevant to the non-comparable acoustic and advection contributions of the numerical dissipation produced by Godunov schemes due to the low Mach number effect.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
The problem of shock-induced collapse of bubbles in liquid is investigated for 3 types of bubble ... more The problem of shock-induced collapse of bubbles in liquid is investigated for 3 types of bubble configuration (bubble row, bubble cluster and bubble matrix) by numerical simulations with a newly developed conservative multi-phase method. The computational results show complex processes which are strongly influenced by the interactions between shock waves, liquid jets, sound waves, vortex sheets and vortices, and bubble oscillations (collapse and rebounce). Some observations and predictions from previous studies are also verified.
DESCRIPTION Dissipation-Dispersion relation for the truncation error of linear and nonlinear fini... more DESCRIPTION Dissipation-Dispersion relation for the truncation error of linear and nonlinear finite difference schemes.
For this study a spatially high-order, shock capturing non-oscillatory finite volume method is co... more For this study a spatially high-order, shock capturing non-oscillatory finite volume method is combined with a weakly compressible flow modeling. As an alternative to methods based on the incompressibility assumption this weakly compressible high-resolution approach is both robust to underresolution and spatially highly accurate. The implicit subgrid-scale (SGS) model permits physically consistent underresolved simulations of incompressible, isotropic turbulent flows at very high Reynolds numbers. Underresolved three-dimensional Taylor-Green vortex (TGV) simulations at finite Reynolds numbers are compared to reference data. Hereby, direct numerical simulation (DNS) data for Re ≤ 3000 is used to assess the accuracy and physical consistency. Large eddy simulation (LES) predictions with two explicit as well as one implicit SGS model help to benchmark the SGS modeling capabilities. The weakly compressible high-resolution approach gives most accurate predictions for the viscous TGV even when resolution is very low. In contrast to the LES our implicit LES predict the laminar-turbulent transition physically consistently. The dissipation rates compare to those of the reference implicit LES, however, at much lower computational costs and mathematical complexity. As our weakly compressible high-resolution approach is designed for the physically consistent simulation of very high Re turbulent flows, an infite Re TGV is studied for an extended period of time. Thereby, the evolution at times beyond the obviously temporary quasi-isotropic state are of particular interest. For the high and infinite Re TGV flows, transition to the isotropic state is observed. Its onset and end are identifiable from a macroscopic energy redistribution within the low-modes. Subsequently, the inertial subrange scales according to E(k) ∝ k −5/3 and is self-similar in time.
In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and de... more In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristicdecomposition approach, the scheme switches between the numerical fluxes with characteristic-wise WENO reconstruction and with the component-wise corresponding optimal linear reconstruction according to a new discontinuity detector. This non-dimensional discontinuity detector measures the resolution limit of the linear scheme and does not degenerate at critical points. A number of numerical examples on inviscid and viscid flow problems computed with 5th-order WENO scheme suggest that, while achieving small numerical dissipation and good robustness, the hybrid scheme generally has the total amount calls for the WENO scheme less than 2%.
The early-time interface instabilities in high intensity (high Weber number and high Reynolds num... more The early-time interface instabilities in high intensity (high Weber number and high Reynolds number) aero-breakup of a liquid drop are investigated by numerical simulations. A combined analysis based on simulation results and linear-instability theory show that both RT (Rayleigh-Taylor) and KH (Kelvin-Helmholtz) instabilities contributes the dominant disturbances originate from about the half way from the stagnation point to the equator. This is verified further with a specially modified simulation, which decreases the effect of KH instability while keeps other flow properties unchanged.
In this work a simple method to enforce the positivity-preserving property for general high-order... more In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed. The method keeps the original scheme unchanged and detects critical numerical fluxes which may lead to negative density and pressure, and then imposes a cutoff flux limiter to satisfy a sufficient condition for preserving positivity. Though an extra time-step size condition is required to maintain the formal order of accuracy, it is less restrictive than those in previous works. A number of numerical examples suggest that this method, when applied on an essentially non-oscillatory base scheme, can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.
For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a proble... more For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificialviscosity-based damping into the momentum conservation equation. Then, operator splitting methods are introduced to discretize the added viscous term for relaxing the time-step limit. To further improve the convergence rate, a random-choice strategy is adopted, in which the viscous term is imposed randomly rather than at every time step. In addition, to avoid the thread-conflict induced by applying shared-memory parallelization to accelerate implicit method, a splitting cell-linked list scheme is devised. A number of benchmark tests suggest that the present method helps systems achieve equilibrium state efficiently.
Comparative evaluation lies at the heart of science, and determining the accuracy of a computatio... more Comparative evaluation lies at the heart of science, and determining the accuracy of a computational method is crucial for evaluating its potential as well as for guiding future efforts. However, metrics that are typically used have inherent shortcomings when faced with the under-resolved solutions of realworld simulation problems. We show how to leverage crowd-sourced user studies in order to address the fundamental problems of widely used classical evaluation metrics. We demonstrate that such user studies, which inherently rely on the human visual system, yield a very robust metric and consistent answers for complex phenomena without any requirements for proficiency regarding the physics at hand. This holds even for cases away from convergence where traditional metrics often end up inconclusive results. More specifically, we evaluate results of different essentially non-oscillatory (ENO) schemes in different fluid flow settings. Our methodology represents a novel and practical approach for scientific evaluations that can give answers for previously unsolved problems.
We have developed a multi-phase SPH method to simulate arbitrary interfaces containing surface ac... more We have developed a multi-phase SPH method to simulate arbitrary interfaces containing surface active agents (surfactants) that locally change the properties of the int erface, such the surface tension coefficient [1]. Our method incorpo rates the effects of surface diffusion, transport of surfactant from/to the bulk phase to/from the interface and diffusion in the bulk phase. Neglecting transport mechanisms, we use this method to study the impact of insoluble surfactants on drop deformati on and breakup in simple shear flow.
Computer Methods in Applied Mechanics and Engineering, 2020
In this paper, we propose a consistent parallel unstructured mesh generator based on a multi-phas... more In this paper, we propose a consistent parallel unstructured mesh generator based on a multi-phase SPH method. A set of physics-motivated modeling equations are developed to achieve the targets of domain decomposition, communication volume optimization and high-quality unstructured mesh generation simultaneously. A unified density field is defined as the target function for both partitioning the geometry and distributing the mesh-vertexes. A multi-phase Smoothing Particle Hydrodynamics (SPH) method is employed to solve the governing equations. All the optimization targets are achieved implicitly and consistently by the particle relaxation procedure without constructing triangulation/tetrahedralization explicitly. The target of communication reduction is achieved by introducing a surface tension model between distinct partitioning sub-domains, which are characterized by colored SPH particles. The resulting partitioning diagram features physically localized sub-domains and optimized interface communication. The target of optimiz
In this paper, we extend the method (Fu et al., [1]) to anisotropic meshes by introducing an adap... more In this paper, we extend the method (Fu et al., [1]) to anisotropic meshes by introducing an adaptive SPH (ASPH) concept with ellipsoidal kernels. First, anisotropic target feature-size and density functions, taking into account the effects of singularities, are defined based on the level-set methodology. Second, ASPH is developed such that the particle distribution relaxes towards the target functions. In order to prevent SPH particles from escaping the mesh generation regions, a ghost surface particle method is proposed in combination with a tailored interaction strategy. Necessary adaptations of supporting numerical algorithms, such as fast neighbor search, for enforcing mesh anisotropy are addressed. Finally, unstructured meshes are generated by an anisotropic Delaunay triangulation conforming to the Riemannian metrics for the resulting particle configuration. The performance of the proposed method is demonstrated by a set of benchmark cases.
A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based ... more A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based on spatial filtering by utilizing smoothed particle hydrodynamics (SPH) approximations. This model is similar to our previous developed SPH dis
We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshles... more We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning subdomains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.
29th International Symposium on Shock Waves 2, 2015
In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenome... more In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenomena in simulating high Mach number flow, and the inaccurate pressure profile in simulating low Mach number flow. We introduced two simple low-Mach-number modifications for the classical Roe flux to decrease the difference between the acoustic and advection contributions of the numerical dissipation. While the first modification increases the local numerical dissipation, the second decreases it. The numerical tests on the double-Mach reflection problem show that both modifications eliminate the kinked Mach stem suffered by the original flux. These results suggest that, other than insufficient numerical dissipation near the shock front, the carbuncle phenomena is strongly relevant to the non-comparable acoustic and advection contributions of the numerical dissipation produced by Godunov schemes due to the low Mach number effect.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
The problem of shock-induced collapse of bubbles in liquid is investigated for 3 types of bubble ... more The problem of shock-induced collapse of bubbles in liquid is investigated for 3 types of bubble configuration (bubble row, bubble cluster and bubble matrix) by numerical simulations with a newly developed conservative multi-phase method. The computational results show complex processes which are strongly influenced by the interactions between shock waves, liquid jets, sound waves, vortex sheets and vortices, and bubble oscillations (collapse and rebounce). Some observations and predictions from previous studies are also verified.
DESCRIPTION Dissipation-Dispersion relation for the truncation error of linear and nonlinear fini... more DESCRIPTION Dissipation-Dispersion relation for the truncation error of linear and nonlinear finite difference schemes.
For this study a spatially high-order, shock capturing non-oscillatory finite volume method is co... more For this study a spatially high-order, shock capturing non-oscillatory finite volume method is combined with a weakly compressible flow modeling. As an alternative to methods based on the incompressibility assumption this weakly compressible high-resolution approach is both robust to underresolution and spatially highly accurate. The implicit subgrid-scale (SGS) model permits physically consistent underresolved simulations of incompressible, isotropic turbulent flows at very high Reynolds numbers. Underresolved three-dimensional Taylor-Green vortex (TGV) simulations at finite Reynolds numbers are compared to reference data. Hereby, direct numerical simulation (DNS) data for Re ≤ 3000 is used to assess the accuracy and physical consistency. Large eddy simulation (LES) predictions with two explicit as well as one implicit SGS model help to benchmark the SGS modeling capabilities. The weakly compressible high-resolution approach gives most accurate predictions for the viscous TGV even when resolution is very low. In contrast to the LES our implicit LES predict the laminar-turbulent transition physically consistently. The dissipation rates compare to those of the reference implicit LES, however, at much lower computational costs and mathematical complexity. As our weakly compressible high-resolution approach is designed for the physically consistent simulation of very high Re turbulent flows, an infite Re TGV is studied for an extended period of time. Thereby, the evolution at times beyond the obviously temporary quasi-isotropic state are of particular interest. For the high and infinite Re TGV flows, transition to the isotropic state is observed. Its onset and end are identifiable from a macroscopic energy redistribution within the low-modes. Subsequently, the inertial subrange scales according to E(k) ∝ k −5/3 and is self-similar in time.
In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and de... more In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristicdecomposition approach, the scheme switches between the numerical fluxes with characteristic-wise WENO reconstruction and with the component-wise corresponding optimal linear reconstruction according to a new discontinuity detector. This non-dimensional discontinuity detector measures the resolution limit of the linear scheme and does not degenerate at critical points. A number of numerical examples on inviscid and viscid flow problems computed with 5th-order WENO scheme suggest that, while achieving small numerical dissipation and good robustness, the hybrid scheme generally has the total amount calls for the WENO scheme less than 2%.
The early-time interface instabilities in high intensity (high Weber number and high Reynolds num... more The early-time interface instabilities in high intensity (high Weber number and high Reynolds number) aero-breakup of a liquid drop are investigated by numerical simulations. A combined analysis based on simulation results and linear-instability theory show that both RT (Rayleigh-Taylor) and KH (Kelvin-Helmholtz) instabilities contributes the dominant disturbances originate from about the half way from the stagnation point to the equator. This is verified further with a specially modified simulation, which decreases the effect of KH instability while keeps other flow properties unchanged.
In this work a simple method to enforce the positivity-preserving property for general high-order... more In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed. The method keeps the original scheme unchanged and detects critical numerical fluxes which may lead to negative density and pressure, and then imposes a cutoff flux limiter to satisfy a sufficient condition for preserving positivity. Though an extra time-step size condition is required to maintain the formal order of accuracy, it is less restrictive than those in previous works. A number of numerical examples suggest that this method, when applied on an essentially non-oscillatory base scheme, can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.
Uploads
Papers by Xiangyu Hu