A Hydra process simulates physical phenomena in a single subdomain for a short duration of simula... more A Hydra process simulates physical phenomena in a single subdomain for a short duration of simulated time. Various phenomena are implemented by different process classes, for example, hydrodynamics (TRISULA), water quality (DELWAQ), and morphology (MORSYS). Each Hydra process stores its state locally in arrays or other appropriate data structures. As stated in the introduction, existing simulation models with only rudimentary modifications for Hydra processes are used. Hydra's primary goal is providing modeling flexibility for the end-user, while striving to minimize the turnaround time of a simulation. Computation, communication and coordination are strictly separated in Hydra. Computation is carried out by legacy simulation processes. Communication between processes is handled by mappers, whose job is to map one process state to another. The coordination of computation and communication in Hydra is done by the executive. The model domain in Hydra can be partitioned into any number, D, of discrete spatial subdomains that need not have the same dimensionality and may overlap. Each subdomain has a computational grid for each process, P. Physical time is divided into discrete time steps, T. This chapter describes work in progress on Delft-Hydra, a framework for simulating a gamut of physical processes related to natural and man-made water systems on concurrent systems. Some of the typical processes are hydrodynamics, morphology, surface waves, chemical reactions, and biological systems. The Hydra architecture contains the notion of an “executive”, whose job is to coordinate the execution of all processes and mappers. Coordination entails scheduling processes so that simulated time advances while state consistency requirements are maintained. The Delft-Hydra architecture has provided quite suitable for coupling existing simulation models, thereby implementing domain decomposition and course-grained parallelism. This gives the end-user more modeling power and reduced computation time when run on a multiprocessor.
ABSTRACT The current generation of operational morphodynamic models is based on the short-wave av... more ABSTRACT The current generation of operational morphodynamic models is based on the short-wave averaged depth-integrated Reynolds equations. Because the short waves are averaged out, a separate module, the wave driver, is needed to provide the wave-depentdent forcing in the momentum equations. Most operational models use a steady wave driver based on linear theory, which means that certain aspects relevant to the sediment transport formulations need to be parametrized. We will present the results of using the phase-resolving Boussinesq-type wave model TRITON as a wave driver, which computes the wave forces. These are transferred to the short-wave averaged free-surface model DELFT3D for the computation of flow, sediment transport, and morphological changes. In this way, the time-integrated effects of intra-wave properties such as individual wave height transformation (including breaking), wave skewness and wave asymmetry, and drift velocities are communicated online with DELFT3D. The changes in bathymetry predicted by DELFT3D are transferred back to TRITON to include this effect in the simulation of the wave dynamics. In particular, we will discuss the online separation of waves into long and short waves (this must be done in time domain to get the time-integrated effects of the intra-wave properties), and reconstruction of the velocity over the vertical coordinate. Validation of the wave part of the methodology is done by comparison with high-resolution wave flume experiments by Boers (1996). The combined strength of both models will improve the prediction capabilities for nearshore morphodynamics in response to wind wave forcing on the time scale of a storm event. This work is funded by the U.S. Office of Naval Research under contract N00014-02-C0075.
International Journal for Numerical Methods in Fluids, Oct 23, 2015
In this work, an approach is proposed for solving the 3D shallow water equations with embedded bo... more In this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut-cell/ghost-cell method is used together with a direction-splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second-order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method.
The boundaries of numerical domains for free-surface wave simulations with marine structures gene... more The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh , in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost.
Predicting the wave exciting forces on a vessel typically involves two separate steps; determinin... more Predicting the wave exciting forces on a vessel typically involves two separate steps; determining a design wave at the location of interest, and then using a linear description of this wave to determine wave forces on a vessel. A method to directly determine the wave exciting forces on a vessel from a wave model would therefore be a very useful tool. This study reports the development, implementation and verification of such a program. The wave model is a non-linear Boussinesq-type 2D model. In determining the wave exciting forces directly from this model, it was desirable to include the non-linear behaviour from the wave model in the determination of the wave forces, as particularly the lower frequency harmonics can have a significant influence on the response of a moored vessel. The conclusion of the study is that the developed program gives a good approximation of the wave exciting forces on a vessel from a non-linear wave field, including the influence of higher and lower order harmonics in the determination of the wave forces.
There are numerous ways to derive a system of 2D Boussinesq‐type wave equations from the 3D poten... more There are numerous ways to derive a system of 2D Boussinesq‐type wave equations from the 3D potential flow equation with free‐surface boundary conditions. This freedom in design is exploited here to derive a Boussinesq‐type model that has a number of unique properties. It ...
ABSTRACT It is shown that a second-order accurate low-order discretization of the steady state co... more ABSTRACT It is shown that a second-order accurate low-order discretization of the steady state compressible Navier-Stokes equations may not lead to an accurate approximation of its solution, and that it is the relative magnitude of truncation error terms rather than the convergence rate of the scheme that is the important parameter deciding the accuracy of prediction of the solution. An approach is adopted to minimize rather than eliminate the low-order truncation errors. Preserving the essential features of the original equations, an optimal low-order conservative discretization scheme is developed which is almost free of numerical diffusion and is fairly insensitive to the grid design. Good results are obtained for the backward facing step problem.
The increasing interest in LNG terminals at nearshore locations has led to the recent Joint Indus... more The increasing interest in LNG terminals at nearshore locations has led to the recent Joint Industry Project (JIP) HAWAI (sHallow WAter Initiative, 2005–2008), a collaboration between MARIN, Single Buoy Moorings, Bureau Veritas, and Deltares (formerly Delft Hydraulics). In this JIP shallow-water wave conditions and their effect on moored vessels were studied. Part of the JIP involved the evaluation of knowledge and numerical models from coastal engineering with respect to their potential for determining shallow-water wave conditions. Operational Boussinesq-type wave models and a long-wave shallow-water model with primary-wave forcing were considered in detail. The former were found to be limited in application due to the limited depth range that can be covered accurately by such models. The latter is considered the most practical and versatile modelling approach that is presently available in coastal engineering for the application considered here. It was used for numerical simulations of a measurement site near the city of Duck (NC, USA). Computed low-frequency wave parameters compare favourably to measured values for three typical primary wave conditions. A comparison of these numerical results with low-frequency wave parameters obtained from the standard approach used in diffraction methods, originally developed for deep water applications, indicates that such a standard approach is not expected to be applicable at shallow-water locations. Detailed local measurements, site-specific numerical calculations and scale-model tests that include the local geometry and the effects of directional spreading, are required to determine the low-frequency wave conditions for design and workability limits at such locations with sufficient detail and accuracy.
International Journal for Numerical Methods in Fluids, Apr 8, 2021
The detailed modeling of free‐surface waves and their interaction with bottom‐mounted or floating... more The detailed modeling of free‐surface waves and their interaction with bottom‐mounted or floating structures requires large computational resources, which is why efficient boundary conditions with low spurious reflection are desirable. The present work presents a review of existing generating‐absorbing boundary conditions (GABCs) for dispersive waves and their reflection characteristics. Hereafter, an adaptation of the classical Sommerfeld condition is proposed by using a depth‐varying coefficient to improve absorption efficiency over a range of wave numbers. An analytical model is proposed to analyse the reflection characteristics for both propagating and evanescent modes, and a considerable improvement in comparison to the Sommerfeld condition is documented over a broad frequency range (reflection coefficients below 5% for nondimensional wave numbers in the range [0, 10]). The new boundary condition is implemented in OpenFoam (waves2Foam) and the functioning for regular, irregular, solitary, and phase‐focused waves is presented.
Instead of developing an adaptive grid technique for some discretization method, we develop a dis... more Instead of developing an adaptive grid technique for some discretization method, we develop a discretization technique designed for grid adaptation. This so-called compatible scheme allows to translate the leading term of the local residual directly in terms of a local error in the numerical solution (the numerical modeling error). An error-dependent smoothing technique is used to ensure that higher-order error terms are negligible. The numerical modeling error is minimized by means of grid adaptation. Fully converged adapted grids with strong local refinements are obtained for a steady-state shallow-water application with a hydraulic jump. An unsteady application confirms the importance of taking the error in time into account when adapting the grid in space. We discuss the shortcomings of the present implementation and the remedies currently under development.
A Hydra process simulates physical phenomena in a single subdomain for a short duration of simula... more A Hydra process simulates physical phenomena in a single subdomain for a short duration of simulated time. Various phenomena are implemented by different process classes, for example, hydrodynamics (TRISULA), water quality (DELWAQ), and morphology (MORSYS). Each Hydra process stores its state locally in arrays or other appropriate data structures. As stated in the introduction, existing simulation models with only rudimentary modifications for Hydra processes are used. Hydra's primary goal is providing modeling flexibility for the end-user, while striving to minimize the turnaround time of a simulation. Computation, communication and coordination are strictly separated in Hydra. Computation is carried out by legacy simulation processes. Communication between processes is handled by mappers, whose job is to map one process state to another. The coordination of computation and communication in Hydra is done by the executive. The model domain in Hydra can be partitioned into any number, D, of discrete spatial subdomains that need not have the same dimensionality and may overlap. Each subdomain has a computational grid for each process, P. Physical time is divided into discrete time steps, T. This chapter describes work in progress on Delft-Hydra, a framework for simulating a gamut of physical processes related to natural and man-made water systems on concurrent systems. Some of the typical processes are hydrodynamics, morphology, surface waves, chemical reactions, and biological systems. The Hydra architecture contains the notion of an “executive”, whose job is to coordinate the execution of all processes and mappers. Coordination entails scheduling processes so that simulated time advances while state consistency requirements are maintained. The Delft-Hydra architecture has provided quite suitable for coupling existing simulation models, thereby implementing domain decomposition and course-grained parallelism. This gives the end-user more modeling power and reduced computation time when run on a multiprocessor.
In this paper the attention is focused on the effect of various VOF methods on efficient and accu... more In this paper the attention is focused on the effect of various VOF methods on efficient and accurate simulation of free surface water waves. For this purpose, we will compare several VOF methods in numerical simulations of propagating waves where strong nonlinear behavior is dominant in the flow. Comparisons and discussions will be provided to underline the significance of free surface modeling on the accuracy of wave propagation.
A Hydra process simulates physical phenomena in a single subdomain for a short duration of simula... more A Hydra process simulates physical phenomena in a single subdomain for a short duration of simulated time. Various phenomena are implemented by different process classes, for example, hydrodynamics (TRISULA), water quality (DELWAQ), and morphology (MORSYS). Each Hydra process stores its state locally in arrays or other appropriate data structures. As stated in the introduction, existing simulation models with only rudimentary modifications for Hydra processes are used. Hydra's primary goal is providing modeling flexibility for the end-user, while striving to minimize the turnaround time of a simulation. Computation, communication and coordination are strictly separated in Hydra. Computation is carried out by legacy simulation processes. Communication between processes is handled by mappers, whose job is to map one process state to another. The coordination of computation and communication in Hydra is done by the executive. The model domain in Hydra can be partitioned into any number, D, of discrete spatial subdomains that need not have the same dimensionality and may overlap. Each subdomain has a computational grid for each process, P. Physical time is divided into discrete time steps, T. This chapter describes work in progress on Delft-Hydra, a framework for simulating a gamut of physical processes related to natural and man-made water systems on concurrent systems. Some of the typical processes are hydrodynamics, morphology, surface waves, chemical reactions, and biological systems. The Hydra architecture contains the notion of an “executive”, whose job is to coordinate the execution of all processes and mappers. Coordination entails scheduling processes so that simulated time advances while state consistency requirements are maintained. The Delft-Hydra architecture has provided quite suitable for coupling existing simulation models, thereby implementing domain decomposition and course-grained parallelism. This gives the end-user more modeling power and reduced computation time when run on a multiprocessor.
ABSTRACT The current generation of operational morphodynamic models is based on the short-wave av... more ABSTRACT The current generation of operational morphodynamic models is based on the short-wave averaged depth-integrated Reynolds equations. Because the short waves are averaged out, a separate module, the wave driver, is needed to provide the wave-depentdent forcing in the momentum equations. Most operational models use a steady wave driver based on linear theory, which means that certain aspects relevant to the sediment transport formulations need to be parametrized. We will present the results of using the phase-resolving Boussinesq-type wave model TRITON as a wave driver, which computes the wave forces. These are transferred to the short-wave averaged free-surface model DELFT3D for the computation of flow, sediment transport, and morphological changes. In this way, the time-integrated effects of intra-wave properties such as individual wave height transformation (including breaking), wave skewness and wave asymmetry, and drift velocities are communicated online with DELFT3D. The changes in bathymetry predicted by DELFT3D are transferred back to TRITON to include this effect in the simulation of the wave dynamics. In particular, we will discuss the online separation of waves into long and short waves (this must be done in time domain to get the time-integrated effects of the intra-wave properties), and reconstruction of the velocity over the vertical coordinate. Validation of the wave part of the methodology is done by comparison with high-resolution wave flume experiments by Boers (1996). The combined strength of both models will improve the prediction capabilities for nearshore morphodynamics in response to wind wave forcing on the time scale of a storm event. This work is funded by the U.S. Office of Naval Research under contract N00014-02-C0075.
International Journal for Numerical Methods in Fluids, Oct 23, 2015
In this work, an approach is proposed for solving the 3D shallow water equations with embedded bo... more In this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut-cell/ghost-cell method is used together with a direction-splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second-order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method.
The boundaries of numerical domains for free-surface wave simulations with marine structures gene... more The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh , in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost.
Predicting the wave exciting forces on a vessel typically involves two separate steps; determinin... more Predicting the wave exciting forces on a vessel typically involves two separate steps; determining a design wave at the location of interest, and then using a linear description of this wave to determine wave forces on a vessel. A method to directly determine the wave exciting forces on a vessel from a wave model would therefore be a very useful tool. This study reports the development, implementation and verification of such a program. The wave model is a non-linear Boussinesq-type 2D model. In determining the wave exciting forces directly from this model, it was desirable to include the non-linear behaviour from the wave model in the determination of the wave forces, as particularly the lower frequency harmonics can have a significant influence on the response of a moored vessel. The conclusion of the study is that the developed program gives a good approximation of the wave exciting forces on a vessel from a non-linear wave field, including the influence of higher and lower order harmonics in the determination of the wave forces.
There are numerous ways to derive a system of 2D Boussinesq‐type wave equations from the 3D poten... more There are numerous ways to derive a system of 2D Boussinesq‐type wave equations from the 3D potential flow equation with free‐surface boundary conditions. This freedom in design is exploited here to derive a Boussinesq‐type model that has a number of unique properties. It ...
ABSTRACT It is shown that a second-order accurate low-order discretization of the steady state co... more ABSTRACT It is shown that a second-order accurate low-order discretization of the steady state compressible Navier-Stokes equations may not lead to an accurate approximation of its solution, and that it is the relative magnitude of truncation error terms rather than the convergence rate of the scheme that is the important parameter deciding the accuracy of prediction of the solution. An approach is adopted to minimize rather than eliminate the low-order truncation errors. Preserving the essential features of the original equations, an optimal low-order conservative discretization scheme is developed which is almost free of numerical diffusion and is fairly insensitive to the grid design. Good results are obtained for the backward facing step problem.
The increasing interest in LNG terminals at nearshore locations has led to the recent Joint Indus... more The increasing interest in LNG terminals at nearshore locations has led to the recent Joint Industry Project (JIP) HAWAI (sHallow WAter Initiative, 2005–2008), a collaboration between MARIN, Single Buoy Moorings, Bureau Veritas, and Deltares (formerly Delft Hydraulics). In this JIP shallow-water wave conditions and their effect on moored vessels were studied. Part of the JIP involved the evaluation of knowledge and numerical models from coastal engineering with respect to their potential for determining shallow-water wave conditions. Operational Boussinesq-type wave models and a long-wave shallow-water model with primary-wave forcing were considered in detail. The former were found to be limited in application due to the limited depth range that can be covered accurately by such models. The latter is considered the most practical and versatile modelling approach that is presently available in coastal engineering for the application considered here. It was used for numerical simulations of a measurement site near the city of Duck (NC, USA). Computed low-frequency wave parameters compare favourably to measured values for three typical primary wave conditions. A comparison of these numerical results with low-frequency wave parameters obtained from the standard approach used in diffraction methods, originally developed for deep water applications, indicates that such a standard approach is not expected to be applicable at shallow-water locations. Detailed local measurements, site-specific numerical calculations and scale-model tests that include the local geometry and the effects of directional spreading, are required to determine the low-frequency wave conditions for design and workability limits at such locations with sufficient detail and accuracy.
International Journal for Numerical Methods in Fluids, Apr 8, 2021
The detailed modeling of free‐surface waves and their interaction with bottom‐mounted or floating... more The detailed modeling of free‐surface waves and their interaction with bottom‐mounted or floating structures requires large computational resources, which is why efficient boundary conditions with low spurious reflection are desirable. The present work presents a review of existing generating‐absorbing boundary conditions (GABCs) for dispersive waves and their reflection characteristics. Hereafter, an adaptation of the classical Sommerfeld condition is proposed by using a depth‐varying coefficient to improve absorption efficiency over a range of wave numbers. An analytical model is proposed to analyse the reflection characteristics for both propagating and evanescent modes, and a considerable improvement in comparison to the Sommerfeld condition is documented over a broad frequency range (reflection coefficients below 5% for nondimensional wave numbers in the range [0, 10]). The new boundary condition is implemented in OpenFoam (waves2Foam) and the functioning for regular, irregular, solitary, and phase‐focused waves is presented.
Instead of developing an adaptive grid technique for some discretization method, we develop a dis... more Instead of developing an adaptive grid technique for some discretization method, we develop a discretization technique designed for grid adaptation. This so-called compatible scheme allows to translate the leading term of the local residual directly in terms of a local error in the numerical solution (the numerical modeling error). An error-dependent smoothing technique is used to ensure that higher-order error terms are negligible. The numerical modeling error is minimized by means of grid adaptation. Fully converged adapted grids with strong local refinements are obtained for a steady-state shallow-water application with a hydraulic jump. An unsteady application confirms the importance of taking the error in time into account when adapting the grid in space. We discuss the shortcomings of the present implementation and the remedies currently under development.
A Hydra process simulates physical phenomena in a single subdomain for a short duration of simula... more A Hydra process simulates physical phenomena in a single subdomain for a short duration of simulated time. Various phenomena are implemented by different process classes, for example, hydrodynamics (TRISULA), water quality (DELWAQ), and morphology (MORSYS). Each Hydra process stores its state locally in arrays or other appropriate data structures. As stated in the introduction, existing simulation models with only rudimentary modifications for Hydra processes are used. Hydra's primary goal is providing modeling flexibility for the end-user, while striving to minimize the turnaround time of a simulation. Computation, communication and coordination are strictly separated in Hydra. Computation is carried out by legacy simulation processes. Communication between processes is handled by mappers, whose job is to map one process state to another. The coordination of computation and communication in Hydra is done by the executive. The model domain in Hydra can be partitioned into any number, D, of discrete spatial subdomains that need not have the same dimensionality and may overlap. Each subdomain has a computational grid for each process, P. Physical time is divided into discrete time steps, T. This chapter describes work in progress on Delft-Hydra, a framework for simulating a gamut of physical processes related to natural and man-made water systems on concurrent systems. Some of the typical processes are hydrodynamics, morphology, surface waves, chemical reactions, and biological systems. The Hydra architecture contains the notion of an “executive”, whose job is to coordinate the execution of all processes and mappers. Coordination entails scheduling processes so that simulated time advances while state consistency requirements are maintained. The Delft-Hydra architecture has provided quite suitable for coupling existing simulation models, thereby implementing domain decomposition and course-grained parallelism. This gives the end-user more modeling power and reduced computation time when run on a multiprocessor.
In this paper the attention is focused on the effect of various VOF methods on efficient and accu... more In this paper the attention is focused on the effect of various VOF methods on efficient and accurate simulation of free surface water waves. For this purpose, we will compare several VOF methods in numerical simulations of propagating waves where strong nonlinear behavior is dominant in the flow. Comparisons and discussions will be provided to underline the significance of free surface modeling on the accuracy of wave propagation.
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Papers by Mart Borsboom