Pub Date : 2024-10-21DOI: 10.1016/j.jcp.2024.113513
Allison M. Carson , Jeffrey W. Banks, William D. Henshaw , Donald W. Schwendeman
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step, three levels in time, and based on the modified equation approach. Second and fourth-order accurate schemes are developed and they incorporate upwind dissipation for stability on overset grids. The fully implicit schemes are useful for certain applications such as the WaveHoltz algorithm for solving Helmholtz problems where very large time-steps are desired. Some wave propagation problems are geometrically stiff due to localized regions of small grid cells, such as grids needed to resolve fine geometric features, and for these situations the implicit time-stepping scheme is combined with an explicit scheme: the implicit scheme is used for component grids containing small cells while the explicit scheme is used on the other grids such as background Cartesian grids. The resulting partitioned implicit-explicit scheme can be many times faster than using an explicit scheme everywhere. The accuracy and stability of the schemes are studied through analysis and numerical computations.
{"title":"High-order accurate implicit-explicit time-stepping schemes for wave equations on overset grids","authors":"Allison M. Carson , Jeffrey W. Banks, William D. Henshaw , Donald W. Schwendeman","doi":"10.1016/j.jcp.2024.113513","DOIUrl":"10.1016/j.jcp.2024.113513","url":null,"abstract":"<div><div>New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step, three levels in time, and based on the modified equation approach. Second and fourth-order accurate schemes are developed and they incorporate upwind dissipation for stability on overset grids. The fully implicit schemes are useful for certain applications such as the WaveHoltz algorithm for solving Helmholtz problems where very large time-steps are desired. Some wave propagation problems are geometrically stiff due to localized regions of small grid cells, such as grids needed to resolve fine geometric features, and for these situations the implicit time-stepping scheme is combined with an explicit scheme: the implicit scheme is used for component grids containing small cells while the explicit scheme is used on the other grids such as background Cartesian grids. The resulting partitioned implicit-explicit scheme can be many times faster than using an explicit scheme everywhere. The accuracy and stability of the schemes are studied through analysis and numerical computations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113513"},"PeriodicalIF":3.8,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-21DOI: 10.1016/j.jcp.2024.113514
Pascal Mossier , Steven Jöns , Simone Chiocchetti , Andrea D. Beck , Claus-Dieter Munz
In this paper, a thermodynamically consistent numerical solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed approximate two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-Bénard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.
{"title":"Numerical simulation of phase transition with the hyperbolic Godunov-Peshkov-Romenski model","authors":"Pascal Mossier , Steven Jöns , Simone Chiocchetti , Andrea D. Beck , Claus-Dieter Munz","doi":"10.1016/j.jcp.2024.113514","DOIUrl":"10.1016/j.jcp.2024.113514","url":null,"abstract":"<div><div>In this paper, a thermodynamically consistent numerical solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed approximate two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-Bénard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113514"},"PeriodicalIF":3.8,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-19DOI: 10.1016/j.jcp.2024.113518
Xi-Qun Lu , Si-Ming Cheng , Li-Ming Yang , Hang Ding , Xi-Yun Lu
In this paper, we propose an algorithm that imposes macroscopic physical constraints with Lagrange multiplier approach in implementing the Maxwell boundary condition within the framework of the discrete velocity method. For the simulation of rarefied gas flows in the presence of solid walls with complex geometry, the distribution function in the reflection region of the wall surface needs to be constructed in the discrete velocity space, to fulfill the specular reflection in the Maxwell boundary condition. The construction process should not consist of interpolation only, but include certain macroscopic physical constraints at the wall surface, so as to correctly account for gas-surface interaction on a macroscopic level. We demonstrate that for the specular reflection, keeping the symmetry of the first three moments of the distribution function between the incident and reflected region is sufficient for maintaining the conservation of mass, momentum, and energy at the wall surface. Furthermore, to strictly satisfy macroscopic physical constraints, a Lagrange multiplier method is introduced into the construction of the distribution function to correct the pure interpolation solution. In addition, the construction process requires the inversion of a large and sparse matrix (of dimension N × N, where N is the number of points in the velocity space). To improve the computational efficiency, the matrix inversion is converted into that of a much smaller matrix, i.e. (D + 2) × (D + 2) in the d-dimensional physical space. A series of numerical experiments are conducted to examine the performance of the proposed algorithm under different flow conditions. We demonstrate that the results obtained by the proposed algorithm are more accurate than the pure interpolation solution, comparing with the benchmark data. Moreover, after the validation of our results with previous studies, we find that the method significantly enhances the conservation of total mass and energy, especially for flows in an enclosed domain.
本文提出了一种在离散速度法框架内实施麦克斯韦边界条件时采用拉格朗日乘法施加宏观物理约束的算法。为了模拟存在复杂几何形状固体壁面的稀薄气体流，需要在离散速度空间中构建壁面反射区域的分布函数，以满足麦克斯韦边界条件中的镜面反射。构建过程不应仅由插值组成，而应包括壁面的某些宏观物理约束，以便在宏观上正确解释气体与壁面的相互作用。我们证明，对于镜面反射，在入射和反射区域之间保持分布函数前三个矩的对称性就足以维持壁面的质量、动量和能量守恒。此外，为了严格满足宏观物理约束，在构建分布函数时引入了拉格朗日乘法，以修正纯插值求解。此外，构建过程需要反演一个大型稀疏矩阵（维度为 N × N，其中 N 为速度空间中的点数）。为了提高计算效率，矩阵反演被转换为更小矩阵的反演，即 d 维物理空间中的 (D + 2) × (D + 2)。我们进行了一系列数值实验，以检验拟议算法在不同流动条件下的性能。与基准数据相比，我们证明了所提算法得到的结果比纯插值解法更精确。此外，在将我们的结果与之前的研究进行验证后，我们发现该方法显著提高了总质量和总能量的守恒性，尤其是对于封闭域中的流动。
{"title":"Maxwell boundary condition for discrete velocity methods: Macroscopic physical constraints and Lagrange multiplier-based implementation","authors":"Xi-Qun Lu , Si-Ming Cheng , Li-Ming Yang , Hang Ding , Xi-Yun Lu","doi":"10.1016/j.jcp.2024.113518","DOIUrl":"10.1016/j.jcp.2024.113518","url":null,"abstract":"<div><div>In this paper, we propose an algorithm that imposes macroscopic physical constraints with Lagrange multiplier approach in implementing the Maxwell boundary condition within the framework of the discrete velocity method. For the simulation of rarefied gas flows in the presence of solid walls with complex geometry, the distribution function in the reflection region of the wall surface needs to be constructed in the discrete velocity space, to fulfill the specular reflection in the Maxwell boundary condition. The construction process should not consist of interpolation only, but include certain macroscopic physical constraints at the wall surface, so as to correctly account for gas-surface interaction on a macroscopic level. We demonstrate that for the specular reflection, keeping the symmetry of the first three moments of the distribution function between the incident and reflected region is sufficient for maintaining the conservation of mass, momentum, and energy at the wall surface. Furthermore, to strictly satisfy macroscopic physical constraints, a Lagrange multiplier method is introduced into the construction of the distribution function to correct the pure interpolation solution. In addition, the construction process requires the inversion of a large and sparse matrix (of dimension <em>N</em> × <em>N</em>, where N is the number of points in the velocity space). To improve the computational efficiency, the matrix inversion is converted into that of a much smaller matrix, i.e. (<em>D</em> + 2) × (<em>D</em> + 2) in the <span>d</span>-dimensional physical space. A series of numerical experiments are conducted to examine the performance of the proposed algorithm under different flow conditions. We demonstrate that the results obtained by the proposed algorithm are more accurate than the pure interpolation solution, comparing with the benchmark data. Moreover, after the validation of our results with previous studies, we find that the method significantly enhances the conservation of total mass and energy, especially for flows in an enclosed domain.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113518"},"PeriodicalIF":3.8,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113512
Xianyi Zeng , Ting Song , Guglielmo Scovazzi
The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shock discontinuities. The SBM belongs to the class of unfitted (or immersed, or embedded) finite element methods and avoids integration over cut cells (and the associated implementation/stability issues) by reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. We specifically discuss the advantages the proposed method offers in avoiding spurious numerical artifacts in two scenarios: (a) when curved boundaries are represented by body-fitted polygonal approximations and (b) when the Kutta condition needs to be imposed in immersed simulations of airfoils. An extensive suite of numerical tests is included.
{"title":"A Shifted Boundary Method for the compressible Euler equations","authors":"Xianyi Zeng , Ting Song , Guglielmo Scovazzi","doi":"10.1016/j.jcp.2024.113512","DOIUrl":"10.1016/j.jcp.2024.113512","url":null,"abstract":"<div><div>The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shock discontinuities. The SBM belongs to the class of unfitted (or immersed, or embedded) finite element methods and avoids integration over cut cells (and the associated implementation/stability issues) by reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. We specifically discuss the advantages the proposed method offers in avoiding spurious numerical artifacts in two scenarios: (a) when curved boundaries are represented by body-fitted polygonal approximations and (b) when the Kutta condition needs to be imposed in immersed simulations of airfoils. An extensive suite of numerical tests is included.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113512"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113511
Jeremy R. Lilly , Giacomo Capodaglio , Darren Engwirda , Robert L. Higdon , Mark R. Petersen
The Courant–Friedrichs–Lewy (CFL) condition is a well known, necessary condition for the stability of explicit time-stepping schemes that effectively places a limit on the size of the largest admittable time-step for a given problem. We formulate and present a new local time-stepping (LTS) scheme optimized, in the CFL sense, for the shallow water equations (SWEs). This new scheme, called FB-LTS, is based on the CFL optimized forward-backward Runge-Kutta schemes from Lilly et al. [16]. We show that FB-LTS maintains exact conservation of mass and absolute vorticity when applied to the TRiSK spatial discretization [21], and provide numerical experiments showing that it retains the temporal order of the scheme on which it is based (second order). We implement FB-LTS, along with a certain operator splitting, in MPAS-Ocean to test computational performance. This scheme, SplitFB-LTS, is up to 10 times faster than the classical four-stage, fourth-order Runge-Kutta method (RK4), and 2.3 times faster than an existing strong stability preserving Runge-Kutta based LTS scheme with the same operator splitting (SplitLTS3). Despite this significant increase in efficiency, the solutions produced by SplitFB-LTS are qualitatively equivalent to those produced by both RK4 and SplitLTS3.
{"title":"Local time-stepping for the shallow water equations using CFL optimized forward-backward Runge-Kutta schemes","authors":"Jeremy R. Lilly , Giacomo Capodaglio , Darren Engwirda , Robert L. Higdon , Mark R. Petersen","doi":"10.1016/j.jcp.2024.113511","DOIUrl":"10.1016/j.jcp.2024.113511","url":null,"abstract":"<div><div>The Courant–Friedrichs–Lewy (CFL) condition is a well known, necessary condition for the stability of explicit time-stepping schemes that effectively places a limit on the size of the largest admittable time-step for a given problem. We formulate and present a new local time-stepping (LTS) scheme optimized, in the CFL sense, for the shallow water equations (SWEs). This new scheme, called FB-LTS, is based on the CFL optimized forward-backward Runge-Kutta schemes from Lilly et al. <span><span>[16]</span></span>. We show that FB-LTS maintains exact conservation of mass and absolute vorticity when applied to the TRiSK spatial discretization <span><span>[21]</span></span>, and provide numerical experiments showing that it retains the temporal order of the scheme on which it is based (second order). We implement FB-LTS, along with a certain operator splitting, in MPAS-Ocean to test computational performance. This scheme, SplitFB-LTS, is up to 10 times faster than the classical four-stage, fourth-order Runge-Kutta method (RK4), and 2.3 times faster than an existing strong stability preserving Runge-Kutta based LTS scheme with the same operator splitting (SplitLTS3). Despite this significant increase in efficiency, the solutions produced by SplitFB-LTS are qualitatively equivalent to those produced by both RK4 and SplitLTS3.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113511"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113499
Ali Akbar Shahbazi , Vahid Esfahanian
Accurate prediction of temperature and Heat Transfer Coefficient (HTC) distributions over gas turbine blades is crucial for the design process and life assessment of these components. Numerical studies of flow over gas turbine blades face significant challenges in accurately simulating two complex phenomena: (1) the transition of flow from laminar to turbulent, and (2) stagnation point flow at the leading edge. Many turbulence models tend to overpredict the temperature on turbine blades, leading to incorrect identification of hot-spot regions and, consequently, erroneous estimations of blade life. This paper investigates the performance of various turbulence models in simulating flow and heat transfer over gas turbine vanes. The study includes three full turbulence models, i.e., Spalart-Allmaras (SA), Shear Stress Transport (SST-kw), and (V2F), as well as two transitional models, i.e., Transition SST (Trans-SST) and (k-kl-w). Simulation results indicate that the , Trans-SST, and models can detect flow transition. However, the transition length and onset location predicted by the Trans-SST and models do not align with experimental data. Conversely, the model suffers from over-predictions at the leading edge due to stagnation point anomaly. To address these issues and due to capacities of the V2F model, this study proposes two modifications to enhance the performance of the V2F model. First, the production term of turbulent kinetic energy is redefined to mitigate the stagnation point anomaly. Second, the model is recalibrated to improve the prediction of flow transition. The new model, named the Production Modified V2F (PMV2F) model, shows promising results in predicting temperature and heat transfer coefficients.
{"title":"Improving turbulence modeling for gas turbine blades: A novel approach to address flow transition and stagnation point anomalies","authors":"Ali Akbar Shahbazi , Vahid Esfahanian","doi":"10.1016/j.jcp.2024.113499","DOIUrl":"10.1016/j.jcp.2024.113499","url":null,"abstract":"<div><div>Accurate prediction of temperature and Heat Transfer Coefficient (HTC) distributions over gas turbine blades is crucial for the design process and life assessment of these components. Numerical studies of flow over gas turbine blades face significant challenges in accurately simulating two complex phenomena: (1) the transition of flow from laminar to turbulent, and (2) stagnation point flow at the leading edge. Many turbulence models tend to overpredict the temperature on turbine blades, leading to incorrect identification of hot-spot regions and, consequently, erroneous estimations of blade life. This paper investigates the performance of various turbulence models in simulating flow and heat transfer over gas turbine vanes. The study includes three full turbulence models, i.e., Spalart-Allmaras (SA), Shear Stress Transport <span><math><mi>k</mi><mo>−</mo><mi>ω</mi></math></span> (SST-kw), and <span><math><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>f</mi></math></span> (V2F), as well as two transitional models, i.e., Transition SST (Trans-SST) and <span><math><mi>k</mi><mo>−</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>L</mi></mrow></msub><mo>−</mo><mi>ω</mi></math></span> (k-kl-w). Simulation results indicate that the <span><math><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>f</mi></math></span>, Trans-SST, and <span><math><mi>k</mi><mo>−</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>L</mi></mrow></msub><mo>−</mo><mi>ω</mi></math></span> models can detect flow transition. However, the transition length and onset location predicted by the Trans-SST and <span><math><mi>k</mi><mo>−</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>L</mi></mrow></msub><mo>−</mo><mi>ω</mi></math></span> models do not align with experimental data. Conversely, the <span><math><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>f</mi></math></span> model suffers from over-predictions at the leading edge due to stagnation point anomaly. To address these issues and due to capacities of the V2F model, this study proposes two modifications to enhance the performance of the V2F model. First, the production term of turbulent kinetic energy is redefined to mitigate the stagnation point anomaly. Second, the model is recalibrated to improve the prediction of flow transition. The new model, named the Production Modified V2F (PMV2F) model, shows promising results in predicting temperature and heat transfer coefficients.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113499"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113516
Magnus Svärd, Henrik Kalisch
Many Boussinesq models suffer from nonlinear instabilities, especially in the context of rapid variations in the bed topography. In this work, a Boussinesq system is put forward which is derived in such a way as to be both linearly and nonlinearly energy-stable.
The proposed system is designed to be robust for coastal simulations with sharply varying bathymetric features while maintaining the dispersive accuracy at any constant depth. For constant bathymetries, the system has the same linear dispersion relation as Peregrine's system ([22]). Furthermore, the system transitions smoothly to the shallow-water system as the depth goes to zero.
In the one-dimensional case, we design a stable finite-volume scheme and demonstrate its robustness, accuracy and stability under grid refinement in a suite of test problems including Dingemans's wave experiment.
Finally, we generalise the system to the two-dimensional case.
{"title":"A novel energy-bounded Boussinesq model and a well balanced and stable numerical discretisation","authors":"Magnus Svärd, Henrik Kalisch","doi":"10.1016/j.jcp.2024.113516","DOIUrl":"10.1016/j.jcp.2024.113516","url":null,"abstract":"<div><div>Many Boussinesq models suffer from nonlinear instabilities, especially in the context of rapid variations in the bed topography. In this work, a Boussinesq system is put forward which is derived in such a way as to be both linearly and nonlinearly energy-stable.</div><div>The proposed system is designed to be robust for coastal simulations with sharply varying bathymetric features while maintaining the dispersive accuracy at any constant depth. For constant bathymetries, the system has the same linear dispersion relation as Peregrine's system (<span><span>[22]</span></span>). Furthermore, the system transitions smoothly to the shallow-water system as the depth goes to zero.</div><div>In the one-dimensional case, we design a stable finite-volume scheme and demonstrate its robustness, accuracy and stability under grid refinement in a suite of test problems including Dingemans's wave experiment.</div><div>Finally, we generalise the system to the two-dimensional case.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113516"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113509
Tim Wegmann , Ansgar Niemöller , Matthias Meinke , Wolfgang Schröder
An Eulerian-Lagrangian coupling method based on hierarchical meshes is presented, which allows an efficient parallelization on high-performance computing hardware. It features an interleaved execution pattern with non-blocking communication, where the hierarchical mesh structure facilitates the redistribution of the computational load. The Lagrangian and Eulerian solvers use hierarchical Cartesian meshes which share a common coarse mesh level. The domain decomposition is based on a space-filling curve defined on the joint computational mesh, where the load is projected to a coarse mesh level used for the partitioning. The performance of the coupled method is evaluated for the problem of spray modeling in turbulent flow. A solution adaptive mesh is utilized for the large-eddy simulation of the flow field and the Lagrangian tracking method is used for the spray particles. Static and dynamic workload estimators are compared with respect to the alleviation of load imbalances. Liquid fuel spray injection in a constant pressure chamber and in an internal combustion engine serves as applications with varying scale resolution and localized computational load. The parallel efficiency of the approach on high performance systems is demonstrated for meshes with up to cells and particles. Detailed performance analyses show a performance gain of the novel algorithm of approx. 20% compared to a non-interleaved time step execution for two-way coupled spray injection simulations. Results of strong scaling experiments at different injection phases show a good parallel performance with an efficiency of up to 81% using 262000 MPI processes.
{"title":"Parallel Eulerian-Lagrangian coupling method on hierarchical meshes","authors":"Tim Wegmann , Ansgar Niemöller , Matthias Meinke , Wolfgang Schröder","doi":"10.1016/j.jcp.2024.113509","DOIUrl":"10.1016/j.jcp.2024.113509","url":null,"abstract":"<div><div>An Eulerian-Lagrangian coupling method based on hierarchical meshes is presented, which allows an efficient parallelization on high-performance computing hardware. It features an interleaved execution pattern with non-blocking communication, where the hierarchical mesh structure facilitates the redistribution of the computational load. The Lagrangian and Eulerian solvers use hierarchical Cartesian meshes which share a common coarse mesh level. The domain decomposition is based on a space-filling curve defined on the joint computational mesh, where the load is projected to a coarse mesh level used for the partitioning. The performance of the coupled method is evaluated for the problem of spray modeling in turbulent flow. A solution adaptive mesh is utilized for the large-eddy simulation of the flow field and the Lagrangian tracking method is used for the spray particles. Static and dynamic workload estimators are compared with respect to the alleviation of load imbalances. Liquid fuel spray injection in a constant pressure chamber and in an internal combustion engine serves as applications with varying scale resolution and localized computational load. The parallel efficiency of the approach on high performance systems is demonstrated for meshes with up to <span><math><mn>2.8</mn><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>9</mn></mrow></msup></math></span> cells and <span><math><mn>21</mn><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup></math></span> particles. Detailed performance analyses show a performance gain of the novel algorithm of approx. 20% compared to a non-interleaved time step execution for two-way coupled spray injection simulations. Results of strong scaling experiments at different injection phases show a good parallel performance with an efficiency of up to 81% using 262000 MPI processes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113509"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Phase-field has been effectively applied to many complex problems according to the mesh based method. However, the computational speed of the numerical method based on phase-field still needs improved. In this paper, an improved localized radial basis function collocation method (LRBFCM) based on the adaptive support domain is employed to the phase-field methods. The proposed adaptive support domain can increase the stability of the LRBFCM, and the improved LRBFCM is much more efficient than the traditional finite element method (FEM) in coupling with phase-field methods. The proposed approach is further applied to the single-phase dendrite solidification, two-phase sintering, and three-phase wetting phenomena. We compare the efficiency of the proposed LRBFCM with different numerical methods, which show that the LRBFCM combined with the Fourier spectral method can deal with the three-phase model with more than ten million nodes easily.
{"title":"The localized radial basis function collocation method for dendritic solidification, solid phase sintering and wetting phenomenon based on phase field","authors":"Pengfei Jiang , Hui Zheng , Jingang Xiong , Timon Rabczuk","doi":"10.1016/j.jcp.2024.113515","DOIUrl":"10.1016/j.jcp.2024.113515","url":null,"abstract":"<div><div>Phase-field has been effectively applied to many complex problems according to the mesh based method. However, the computational speed of the numerical method based on phase-field still needs improved. In this paper, an improved localized radial basis function collocation method (LRBFCM) based on the adaptive support domain is employed to the phase-field methods. The proposed adaptive support domain can increase the stability of the LRBFCM, and the improved LRBFCM is much more efficient than the traditional finite element method (FEM) in coupling with phase-field methods. The proposed approach is further applied to the single-phase dendrite solidification, two-phase sintering, and three-phase wetting phenomena. We compare the efficiency of the proposed LRBFCM with different numerical methods, which show that the LRBFCM combined with the Fourier spectral method can deal with the three-phase model with more than ten million nodes easily.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113515"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113510
David Sidilkover
Lagrangian methods for computational continuum mechanics, since their inception, traditionally relied on staggered meshes. This feature, while facilitating their robustness and reliability, presented some difficulties. The latter motivated the search for collocated Lagrangian schemes. One of the attempts to develop such a scheme was the CAVEAT method/code. Numerical solutions produced by this method suffered sometimes from large vorticity errors, which could lead to mesh entanglement and premature run termination. The efforts to devise a more robust collocated scheme began to bear fruit a couple of decades later starting from the groundbreaking method GLACE, closely followed by EUCCLHYD and later on by CCH and others.
One of the aims of this paper is to present a novel Lagrangian collocated factorizable scheme. The notion of a factorizable method was introduced more than two decades ago within the Eulerian approach. It designates a numerical scheme that reflects/preserves the mixed character of the Euler equations, i.e. does not introduce non-physical coupling between the different factors of the system of equations - advection and acoustics operators.
Another aim of this paper is to explore the connection between the factorizability property of a Lagrangian method and whether or not it suffers from spurious vorticity. Several existing schemes are surveyed for this purpose. A conjecture summarizing our findings is formulated.
{"title":"Spurious vorticity in Eulerian and Lagrangian methods","authors":"David Sidilkover","doi":"10.1016/j.jcp.2024.113510","DOIUrl":"10.1016/j.jcp.2024.113510","url":null,"abstract":"<div><div>Lagrangian methods for computational continuum mechanics, since their inception, traditionally relied on staggered meshes. This feature, while facilitating their robustness and reliability, presented some difficulties. The latter motivated the search for collocated Lagrangian schemes. One of the attempts to develop such a scheme was the CAVEAT method/code. Numerical solutions produced by this method suffered sometimes from large vorticity errors, which could lead to mesh entanglement and premature run termination. The efforts to devise a more robust collocated scheme began to bear fruit a couple of decades later starting from the groundbreaking method GLACE, closely followed by EUCCLHYD and later on by CCH and others.</div><div>One of the aims of this paper is to present a novel Lagrangian collocated <em>factorizable</em> scheme. The notion of a <em>factorizable</em> method was introduced more than two decades ago within the Eulerian approach. It designates a numerical scheme that reflects/preserves the mixed character of the Euler equations, i.e. does not introduce non-physical coupling between the different factors of the system of equations - advection and acoustics operators.</div><div>Another aim of this paper is to explore the connection between the <em>factorizability</em> property of a Lagrangian method and whether or not it suffers from spurious vorticity. Several existing schemes are surveyed for this purpose. A conjecture summarizing our findings is formulated.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113510"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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