Journal of Computational Physics最新文献

{"title":"Symmetric form of the magnetohydrodynamics equations","authors":"S.K. Godunov","doi":"10.1016/j.jcp.2024.113523","DOIUrl":"10.1016/j.jcp.2024.113523","url":null,"abstract":"<div><div>It is well known that many linear hyperbolic systems of mathematical physics are symmetric hyperbolic systems. In the case of nonlinear equations, the question of whether they can be written in symmetric form is far from simple.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113523"},"PeriodicalIF":3.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560649","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}

{"title":"Interesting class of quasilinear systems","authors":"S.K. Godunov","doi":"10.1016/j.jcp.2024.113521","DOIUrl":"10.1016/j.jcp.2024.113521","url":null,"abstract":"<div><div>With this work, I want to draw attention to a class of differential equations that encompasses a number of important equations of mathematical physics and is convenient for constructing a mathematical theory.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113521"},"PeriodicalIF":3.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536283","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}

{"title":"A fully-coupled algorithm with implicit surface tension treatment for interfacial flows with large density ratios","authors":"Romain Janodet ,&nbsp;Berend van Wachem ,&nbsp;Fabian Denner","doi":"10.1016/j.jcp.2024.113520","DOIUrl":"10.1016/j.jcp.2024.113520","url":null,"abstract":"<div><div>The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with moderate inertia. To date, the majority of interfacial-flow simulations are performed using an explicit surface-tension treatment, which restrains the performance of such simulations. Recently, an implicit treatment of surface tension able to breach the capillary time-step constraint using the volume-of-fluid (VOF) method was proposed, based on a fully-coupled pressure-based finite-volume algorithm. To this end, the interface-advection equation is incorporated implicitly into the linear flow solver, resulting in a tight coupling between all implicit solution variables (colour function, pressure, velocity). However, this algorithm is limited to uniform density and viscosity fields. Here, we present a fully-coupled algorithm for interfacial flows with implicit surface tension applicable to interfacial flows with large density and viscosity ratios. This is achieved by solving the continuity and momentum equations in conservative form, whereby the density is treated implicitly with respect to the colour function, and the advection term of the interface-advection equation is discretised using the THINC/QQ algebraic VOF scheme, yielding a consistent discretisation of the advective terms. This new algorithm is tested by considering representative surface-tension-dominated interfacial flows, including the Laplace equilibrium of a stationary droplet and the three-dimensional Rayleigh-Plateau instability of a liquid filament. The presented results demonstrate that interfacial flows with large density and viscosity ratios can be simulated and energy conservation is ensured, even with a time step larger than the capillary time-step constraint, provided that other time-step restrictions are satisfied.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113520"},"PeriodicalIF":3.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536280","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}

{"title":"Memoirs of finite difference schemes","authors":"S.K. Godunov","doi":"10.1016/j.jcp.2024.113522","DOIUrl":"10.1016/j.jcp.2024.113522","url":null,"abstract":"<div><div>The report contains recollections of the invention of one of the methods for solving gas dynamics equations (1953 - 1969). Serious attention is given to questions for which answers are still unknown to this day. This report is intended for researchers, engineers, and those interested in the history of mathematics.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113522"},"PeriodicalIF":3.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554357","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}

{"title":"High-order accurate implicit-explicit time-stepping schemes for wave equations on overset grids","authors":"Allison M. Carson ,&nbsp;Jeffrey W. Banks,&nbsp;William D. Henshaw ,&nbsp;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}

{"title":"Numerical simulation of phase transition with the hyperbolic Godunov-Peshkov-Romenski model","authors":"Pascal Mossier ,&nbsp;Steven Jöns ,&nbsp;Simone Chiocchetti ,&nbsp;Andrea D. Beck ,&nbsp;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}

{"title":"Maxwell boundary condition for discrete velocity methods: Macroscopic physical constraints and Lagrange multiplier-based implementation","authors":"Xi-Qun Lu ,&nbsp;Si-Ming Cheng ,&nbsp;Li-Ming Yang ,&nbsp;Hang Ding ,&nbsp;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}

{"title":"A Shifted Boundary Method for the compressible Euler equations","authors":"Xianyi Zeng ,&nbsp;Ting Song ,&nbsp;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}

{"title":"Local time-stepping for the shallow water equations using CFL optimized forward-backward Runge-Kutta schemes","authors":"Jeremy R. Lilly ,&nbsp;Giacomo Capodaglio ,&nbsp;Darren Engwirda ,&nbsp;Robert L. Higdon ,&nbsp;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}

{"title":"Improving turbulence modeling for gas turbine blades: A novel approach to address flow transition and stagnation point anomalies","authors":"Ali Akbar Shahbazi ,&nbsp;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}