Waves are pivotal factors in coastal areas, and effective simulation of wave-related phenomena is crucial. This paper presents the extension of the non-hydrostatic model from single-layer σ transformation to double-layer σ transformation in order to stabilize submerged structures and jet orifices under wave environment. The Lagrangian-Eulerian method is adopted for tracking the free surface in this model. This updated model is validated through comparisons against a series of test cases, including wave structure interaction and horizontal jet under waves. A good agreement between the model results and experimental data is achieved, demonstrating the capability of the developed model to fix the submerged object to resolve wave-structure and wave-jet interactions. Thus, the proposed double-layer σ model can be seen as a useful tool to simulate problems in coastal dynamics.
{"title":"A double-layer non-hydrostatic model for simulating wave-structure and wave-jet interactions","authors":"Yuhang Chen , Yongping Chen , Zhenshan Xu , Pengzhi Lin , Zhihua Xie","doi":"10.1016/j.jcp.2024.113634","DOIUrl":"10.1016/j.jcp.2024.113634","url":null,"abstract":"<div><div>Waves are pivotal factors in coastal areas, and effective simulation of wave-related phenomena is crucial. This paper presents the extension of the non-hydrostatic model from single-layer <em>σ</em> transformation to double-layer <em>σ</em> transformation in order to stabilize submerged structures and jet orifices under wave environment. The Lagrangian-Eulerian method is adopted for tracking the free surface in this model. This updated model is validated through comparisons against a series of test cases, including wave structure interaction and horizontal jet under waves. A good agreement between the model results and experimental data is achieved, demonstrating the capability of the developed model to fix the submerged object to resolve wave-structure and wave-jet interactions. Thus, the proposed double-layer <em>σ</em> model can be seen as a useful tool to simulate problems in coastal dynamics.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113634"},"PeriodicalIF":3.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142758987","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 : 2024-11-29DOI: 10.1016/j.jcp.2024.113632
Jason Goulding, Tamar Shinar, Craig Schroeder
The Cahn-Hilliard equation describes phase separation in a binary mixture, typically modeled with a phase variable that represents the concentration of one phase or the concentration difference between the two phases. Though the system is energetically driven toward solutions within the physically meaningful range of the phase variable, numerical methods often struggle to maintain these bounds, leading to physically invalid quantities and numerical difficulties. In this work, we introduce a novel splitting and discretization for the Cahn-Hilliard equation, coupled with the Navier-Stokes equations, which inherently preserves the bounds of the phase variable. This approach transforms the fourth-order Cahn-Hilliard equation into a second-order Helmholtz equation and a second-order nonlinear equation with implicit energy barriers, which is reformulated and solved with a safeguarded optimization-based solution method. Our scheme ensures the phase variable remains in the valid range, robustly handles large density ratios, conserves mass and momentum, maintains consistency between these quantities, and achieves second-order accuracy. We demonstrate the method's effectiveness through a variety of studies of two-dimensional, two-phase fluid mixtures.
{"title":"Conservative, bounded, and nonlinear discretization of the Cahn-Hilliard-Navier-Stokes equations","authors":"Jason Goulding, Tamar Shinar, Craig Schroeder","doi":"10.1016/j.jcp.2024.113632","DOIUrl":"10.1016/j.jcp.2024.113632","url":null,"abstract":"<div><div>The Cahn-Hilliard equation describes phase separation in a binary mixture, typically modeled with a phase variable that represents the concentration of one phase or the concentration difference between the two phases. Though the system is energetically driven toward solutions within the physically meaningful range of the phase variable, numerical methods often struggle to maintain these bounds, leading to physically invalid quantities and numerical difficulties. In this work, we introduce a novel splitting and discretization for the Cahn-Hilliard equation, coupled with the Navier-Stokes equations, which inherently preserves the bounds of the phase variable. This approach transforms the fourth-order Cahn-Hilliard equation into a second-order Helmholtz equation and a second-order nonlinear equation with implicit energy barriers, which is reformulated and solved with a safeguarded optimization-based solution method. Our scheme ensures the phase variable remains in the valid range, robustly handles large density ratios, conserves mass and momentum, maintains consistency between these quantities, and achieves second-order accuracy. We demonstrate the method's effectiveness through a variety of studies of two-dimensional, two-phase fluid mixtures.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113632"},"PeriodicalIF":3.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142758985","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 : 2024-11-29DOI: 10.1016/j.jcp.2024.113633
Pranshul Thakur, Siva Nadarajah
Solutions to the governing partial differential equations obtained from a discrete numerical scheme can have significant errors, especially near shocks where the discrete representation of the solution cannot fully capture the discontinuity in the solution. Recent approaches of shock tracking [1], [2] implicitly align the faces of mesh elements with the shock, yielding accurate solutions on coarse meshes. In engineering applications, the solution field is often used to evaluate a scalar functional of interest, such as lift or drag over an airfoil. While functionals are sensitive to errors in the flow solution, certain regions in the domain are more important for accurate evaluation of the functional than the rest. Using this fact, we formulate a goal-oriented implicit shock tracking approach that captures a segment of the discontinuity that is important for evaluating the functional. Shock tracking is achieved using the Lagrange-Newton-Krylov-Schur (LNKS) full space optimizer to minimize the adjoint-weighted residual error indicator. We also present a method to evaluate the sensitivity and the Hessian of the functional error. Using available block preconditioners for LNKS [3], [4] makes the full space approach scalable. The method is applied to test cases of two-dimensional advection and inviscid compressible flows to demonstrate functional-dependent shock tracking. Tracking the entire shock without using artificial dissipation results in the error converging at the orders of .
{"title":"Adjoint-based goal-oriented implicit shock tracking using full space mesh optimization","authors":"Pranshul Thakur, Siva Nadarajah","doi":"10.1016/j.jcp.2024.113633","DOIUrl":"10.1016/j.jcp.2024.113633","url":null,"abstract":"<div><div>Solutions to the governing partial differential equations obtained from a discrete numerical scheme can have significant errors, especially near shocks where the discrete representation of the solution cannot fully capture the discontinuity in the solution. Recent approaches of shock tracking <span><span>[1]</span></span>, <span><span>[2]</span></span> implicitly align the faces of mesh elements with the shock, yielding accurate solutions on coarse meshes. In engineering applications, the solution field is often used to evaluate a scalar functional of interest, such as lift or drag over an airfoil. While functionals are sensitive to errors in the flow solution, certain regions in the domain are more important for accurate evaluation of the functional than the rest. Using this fact, we formulate a goal-oriented implicit shock tracking approach that captures a segment of the discontinuity that is important for evaluating the functional. Shock tracking is achieved using the Lagrange-Newton-Krylov-Schur (LNKS) full space optimizer to minimize the adjoint-weighted residual error indicator. We also present a method to evaluate the sensitivity and the Hessian of the functional error. Using available block preconditioners for LNKS <span><span>[3]</span></span>, <span><span>[4]</span></span> makes the full space approach scalable. The method is applied to test cases of two-dimensional advection and inviscid compressible flows to demonstrate functional-dependent shock tracking. Tracking the entire shock without using artificial dissipation results in the error converging at the orders of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113633"},"PeriodicalIF":3.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142758986","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 : 2024-11-28DOI: 10.1016/j.jcp.2024.113630
Guangliang Zhang , Haijian Yang , Tianpei Cheng , Chao Yang
The primal-dual active-set (PDAS) algorithm is a well-established and efficient method for addressing complementarity problems. However, the majority of existing approaches primarily concentrate on solving this non-smooth system with linear cases, and the straightforward extension of the primal-dual active-set method for solving nonlinear large-scale engineering problems does not work as well as expected, due to the unbalanced nonlinearities that bring about the difficulty of the slow convergence or stagnation. In the paper, we present the primal-dual active-set method with backtracking on the parallel computing framework for solving the nonlinear complementarity problem (NCP) arising from the discretization of partial differential equations. Some adaptive nonlinear preconditioning strategies based on nonlinear elimination are presented to handle the high nonlinearity of the nonsmooth system, and a family of linear preconditioners based on domain decomposition is developed to enhance the efficiency and scalability of this Newton-type method. Moreover, rigorous proof to establish both the monotone and superlinear convergence of the primal-dual active-set algorithm is also provided for the theoretical analysis. A series of numerical experiments for a family of multiphase reservoir problems, i.e., the CO2 injection model, are carried out to demonstrate the robustness and efficiency of the proposed parallel algorithm.
{"title":"Parallel primal-dual active-set algorithm with nonlinear and linear preconditioners","authors":"Guangliang Zhang , Haijian Yang , Tianpei Cheng , Chao Yang","doi":"10.1016/j.jcp.2024.113630","DOIUrl":"10.1016/j.jcp.2024.113630","url":null,"abstract":"<div><div>The primal-dual active-set (PDAS) algorithm is a well-established and efficient method for addressing complementarity problems. However, the majority of existing approaches primarily concentrate on solving this non-smooth system with linear cases, and the straightforward extension of the primal-dual active-set method for solving nonlinear large-scale engineering problems does not work as well as expected, due to the unbalanced nonlinearities that bring about the difficulty of the slow convergence or stagnation. In the paper, we present the primal-dual active-set method with backtracking on the parallel computing framework for solving the nonlinear complementarity problem (NCP) arising from the discretization of partial differential equations. Some adaptive nonlinear preconditioning strategies based on nonlinear elimination are presented to handle the high nonlinearity of the nonsmooth system, and a family of linear preconditioners based on domain decomposition is developed to enhance the efficiency and scalability of this Newton-type method. Moreover, rigorous proof to establish both the monotone and superlinear convergence of the primal-dual active-set algorithm is also provided for the theoretical analysis. A series of numerical experiments for a family of multiphase reservoir problems, i.e., the CO<sub>2</sub> injection model, are carried out to demonstrate the robustness and efficiency of the proposed parallel algorithm.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113630"},"PeriodicalIF":3.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747021","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 : 2024-11-28DOI: 10.1016/j.jcp.2024.113624
Justin Kin Jun Hew , Kenneth Duru , Stephen Roberts , Christopher Zoppou , Kieran Ricardo
We present an energy/entropy stable and high order accurate finite difference (FD) method for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant form using the newly developed dual-pairing and dispersion-relation preserving summation by parts (SBP) FD operators. We derive new well-posed boundary conditions (BCs) for the SWE in one space dimension, formulated in terms of fluxes and applicable to linear and nonlinear SWEs. For the nonlinear vector invariant SWE in the subcritical regime, where energy is an entropy functional, we find that energy/entropy stability ensures the boundedness of numerical solution but does not guarantee convergence. Adequate amount of numerical dissipation is necessary to control high frequency errors which could negatively impact accuracy in the numerical simulations. Using the dual-pairing SBP framework, we derive high order accurate and nonlinear hyper-viscosity operator which dissipates entropy and enstrophy. The hyper-viscosity operator effectively minimises oscillations from shocks and discontinuities, and eliminates high frequency grid-scale errors. The numerical method is most suitable for the simulations of subcritical flows typically observed in atmospheric and geostrophic flow problems. We prove both nonlinear and local linear stability results, as well as a priori error estimates for the semi-discrete approximations of both linear and nonlinear SWEs. Convergence, accuracy, and well-balanced properties are verified via the method of manufactured solutions and canonical test problems such as the dam break and lake at rest. Numerical simulations in two-dimensions are presented which include the rotating and merging vortex problem and barotropic shear instability, with fully developed turbulence.
{"title":"Strongly stable dual-pairing summation by parts finite difference schemes for the vector invariant nonlinear shallow water equations – I: Numerical scheme and validation on the plane","authors":"Justin Kin Jun Hew , Kenneth Duru , Stephen Roberts , Christopher Zoppou , Kieran Ricardo","doi":"10.1016/j.jcp.2024.113624","DOIUrl":"10.1016/j.jcp.2024.113624","url":null,"abstract":"<div><div>We present an energy/entropy stable and high order accurate finite difference (FD) method for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant form using the newly developed dual-pairing and dispersion-relation preserving summation by parts (SBP) FD operators. We derive new well-posed boundary conditions (BCs) for the SWE in one space dimension, formulated in terms of fluxes and applicable to linear and nonlinear SWEs. For the nonlinear vector invariant SWE in the subcritical regime, where energy is an entropy functional, we find that energy/entropy stability ensures the boundedness of numerical solution but does not guarantee convergence. Adequate amount of numerical dissipation is necessary to control high frequency errors which could negatively impact accuracy in the numerical simulations. Using the dual-pairing SBP framework, we derive high order accurate and nonlinear hyper-viscosity operator which dissipates entropy and enstrophy. The hyper-viscosity operator effectively minimises oscillations from shocks and discontinuities, and eliminates high frequency grid-scale errors. The numerical method is most suitable for the simulations of subcritical flows typically observed in atmospheric and geostrophic flow problems. We prove both nonlinear and local linear stability results, as well as a priori error estimates for the semi-discrete approximations of both linear and nonlinear SWEs. Convergence, accuracy, and well-balanced properties are verified via the method of manufactured solutions and canonical test problems such as the dam break and lake at rest. Numerical simulations in two-dimensions are presented which include the rotating and merging vortex problem and barotropic shear instability, with fully developed turbulence.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113624"},"PeriodicalIF":3.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747019","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 : 2024-11-26DOI: 10.1016/j.jcp.2024.113623
Jamie M. Taylor , Manuela Bastidas , David Pardo , Ignacio Muga
Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used machine learning tools, and in those models, the choice of an appropriate loss function is critical. In general, the main goal is to guarantee that minimizing the loss during training translates to minimizing the error in the solution at the same rate. In this work, we focus on the time-harmonic Maxwell's equations, whose weak formulation takes as the space of test functions. We propose a NN in which the loss function is a computable approximation of the dual norm of the weak-form PDE residual. To that end, we employ the Helmholtz decomposition of the space and construct an orthonormal basis for this space in two and three spatial dimensions. Here, we use the Discrete Sine/Cosine Transform to accurately and efficiently compute the discrete version of our proposed loss function. Moreover, in the numerical examples we show a high correlation between the proposed loss function and the H(curl)-norm of the error, even in problems with low-regularity solutions.
{"title":"Deep Fourier Residual method for solving time-harmonic Maxwell's equations","authors":"Jamie M. Taylor , Manuela Bastidas , David Pardo , Ignacio Muga","doi":"10.1016/j.jcp.2024.113623","DOIUrl":"10.1016/j.jcp.2024.113623","url":null,"abstract":"<div><div>Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used machine learning tools, and in those models, the choice of an appropriate loss function is critical. In general, the main goal is to guarantee that minimizing the loss during training translates to minimizing the error in the solution at the same rate. In this work, we focus on the time-harmonic Maxwell's equations, whose weak formulation takes <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mrow><mi>curl</mi></mrow><mo>,</mo><mi>Ω</mi><mo>)</mo></math></span> as the space of test functions. We propose a NN in which the loss function is a computable approximation of the dual norm of the weak-form PDE residual. To that end, we employ the Helmholtz decomposition of the space <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mrow><mi>curl</mi></mrow><mo>,</mo><mi>Ω</mi><mo>)</mo></math></span> and construct an orthonormal basis for this space in two and three spatial dimensions. Here, we use the Discrete Sine/Cosine Transform to accurately and efficiently compute the discrete version of our proposed loss function. Moreover, in the numerical examples we show a high correlation between the proposed loss function and the <em>H</em>(curl)-norm of the error, even in problems with low-regularity solutions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113623"},"PeriodicalIF":3.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747020","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 : 2024-11-26DOI: 10.1016/j.jcp.2024.113622
Arpit Babbar, Praveen Chandrashekar
Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. This work extends the LWFR scheme to solve conservation laws on curvilinear meshes with adaptive mesh refinement (AMR). The scheme uses a subcell based blending limiter to perform shock capturing and exploits the same subcell structure to obtain admissibility preservation on curvilinear meshes. It is proven that the proposed extension of LWFR scheme to curvilinear grids preserves constant solution (free stream preservation) under the standard metric identities. For curvilinear meshes, linear Fourier stability analysis cannot be used to obtain an optimal CFL number. Thus, an embedded-error based time step computation method is proposed for LWFR method which reduces fine-tuning process required to select a stable CFL number using the wave speed based time step computation. The developments are tested on compressible Euler's equations, validating the blending limiter, admissibility preservation, AMR algorithm, curvilinear meshes and error based time stepping.
{"title":"Lax-Wendroff flux reconstruction on adaptive curvilinear meshes with error based time stepping for hyperbolic conservation laws","authors":"Arpit Babbar, Praveen Chandrashekar","doi":"10.1016/j.jcp.2024.113622","DOIUrl":"10.1016/j.jcp.2024.113622","url":null,"abstract":"<div><div>Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. This work extends the LWFR scheme to solve conservation laws on curvilinear meshes with adaptive mesh refinement (AMR). The scheme uses a subcell based blending limiter to perform shock capturing and exploits the same subcell structure to obtain admissibility preservation on curvilinear meshes. It is proven that the proposed extension of LWFR scheme to curvilinear grids preserves constant solution (free stream preservation) under the standard metric identities. For curvilinear meshes, linear Fourier stability analysis cannot be used to obtain an optimal CFL number. Thus, an embedded-error based time step computation method is proposed for LWFR method which reduces fine-tuning process required to select a stable CFL number using the wave speed based time step computation. The developments are tested on compressible Euler's equations, validating the blending limiter, admissibility preservation, AMR algorithm, curvilinear meshes and error based time stepping.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113622"},"PeriodicalIF":3.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743161","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 : 2024-11-26DOI: 10.1016/j.jcp.2024.113620
Yan Tan , Jun Zhu , Chi-Wang Shu , Jianxian Qiu
{"title":"Letter to Editor: Regarding the numerical results in “A novel finite-difference converged ENO scheme for steady-state simulations of Euler equations”, by Tian Liang and Lin Fu, Journal of Computational Physics, 519 (2024), 113386","authors":"Yan Tan , Jun Zhu , Chi-Wang Shu , Jianxian Qiu","doi":"10.1016/j.jcp.2024.113620","DOIUrl":"10.1016/j.jcp.2024.113620","url":null,"abstract":"","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113620"},"PeriodicalIF":3.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723646","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 : 2024-11-26DOI: 10.1016/j.jcp.2024.113619
Ruo Li , Yixiao Lu , Yanli Wang
This paper presents an asymptotic preserving (AP) implicit-explicit (IMEX) scheme for solving the quantum BGK equation using the Hermite spectral method. The distribution function is expanded in a series of Hermite polynomials, with the Gaussian function serving as the weight function. The main challenge in this numerical scheme lies in efficiently expanding the quantum Maxwellian with the Hermite basis functions. To overcome this, we simplify the problem to the calculation of polylogarithms and propose an efficient algorithm to handle it, utilizing the Gauss-Hermite quadrature. Several numerical simulations, including a spatially 2D lid-driven cavity flow, demonstrate the AP property and remarkable efficiency of this method.
{"title":"A highly efficient asymptotic preserving IMEX method for the quantum BGK equation","authors":"Ruo Li , Yixiao Lu , Yanli Wang","doi":"10.1016/j.jcp.2024.113619","DOIUrl":"10.1016/j.jcp.2024.113619","url":null,"abstract":"<div><div>This paper presents an asymptotic preserving (AP) implicit-explicit (IMEX) scheme for solving the quantum BGK equation using the Hermite spectral method. The distribution function is expanded in a series of Hermite polynomials, with the Gaussian function serving as the weight function. The main challenge in this numerical scheme lies in efficiently expanding the quantum Maxwellian with the Hermite basis functions. To overcome this, we simplify the problem to the calculation of polylogarithms and propose an efficient algorithm to handle it, utilizing the Gauss-Hermite quadrature. Several numerical simulations, including a spatially 2D lid-driven cavity flow, demonstrate the AP property and remarkable efficiency of this method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113619"},"PeriodicalIF":3.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743159","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 : 2024-11-26DOI: 10.1016/j.jcp.2024.113618
Luan F. Santos , Joseph Mouallem , Pedro S. Peixoto
The cubed-sphere finite-volume dynamical core (FV3), developed by GFDL-NOAA-USA, serves as the dynamical core for many models worldwide. In 2019, it was officially designated as the dynamical core for the new Global Forecast System of the National Weather Service in the USA, replacing the spectral model. The finite-volume approach employed by FV3 to solve horizontal dynamics involves the application of transport finite-volume fluxes for different variables. Hence, the transport scheme plays a key role in the model. Therefore, this work proposes to revisit the details of the transport scheme of FV3 with the aim of adding enhancements. We proposed modifications to the FV3 transport scheme, which notably enhanced accuracy, particularly in the presence of divergent winds, as evidenced by numerical experiments. In contrast to the FV3 scheme's first-order accuracy in the presence of divergent winds, the proposed scheme achieves second-order accuracy. For divergence-free winds, both schemes are second-order, with our scheme being slightly more accurate. Additionally, the proposed scheme exhibits slight computational overhead but is easily implemented in the current code. In summary, the proposed scheme offers significant improvements in accuracy, particularly in the presence of divergent winds, which are present in various atmospheric phenomena, while maintaining computational efficiency.
{"title":"Analysis of finite-volume transport schemes on cubed-sphere grids and an accurate scheme for divergent winds","authors":"Luan F. Santos , Joseph Mouallem , Pedro S. Peixoto","doi":"10.1016/j.jcp.2024.113618","DOIUrl":"10.1016/j.jcp.2024.113618","url":null,"abstract":"<div><div>The cubed-sphere finite-volume dynamical core (FV3), developed by GFDL-NOAA-USA, serves as the dynamical core for many models worldwide. In 2019, it was officially designated as the dynamical core for the new Global Forecast System of the National Weather Service in the USA, replacing the spectral model. The finite-volume approach employed by FV3 to solve horizontal dynamics involves the application of transport finite-volume fluxes for different variables. Hence, the transport scheme plays a key role in the model. Therefore, this work proposes to revisit the details of the transport scheme of FV3 with the aim of adding enhancements. We proposed modifications to the FV3 transport scheme, which notably enhanced accuracy, particularly in the presence of divergent winds, as evidenced by numerical experiments. In contrast to the FV3 scheme's first-order accuracy in the presence of divergent winds, the proposed scheme achieves second-order accuracy. For divergence-free winds, both schemes are second-order, with our scheme being slightly more accurate. Additionally, the proposed scheme exhibits slight computational overhead but is easily implemented in the current code. In summary, the proposed scheme offers significant improvements in accuracy, particularly in the presence of divergent winds, which are present in various atmospheric phenomena, while maintaining computational efficiency.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113618"},"PeriodicalIF":3.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723643","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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