Journal of Computational Physics最新文献

{"title":"A discontinuous Galerkin method for free surface flows with fluid-solid interaction","authors":"Raj Kumar Pal ,&nbsp;Giang Huynh ,&nbsp;Reza Abedi","doi":"10.1016/j.jcp.2025.114185","DOIUrl":"10.1016/j.jcp.2025.114185","url":null,"abstract":"<div><div>This paper presents a monolithic and a partitioned Arbitrary Lagrangian Eulerian (ALE) method for free surface flows over immersed movable rigid bodies. A discontinuous Galerkin (DG) method is used to discretize the incompressible Navier-Stokes equations, while rigid body equations are used to model the motion of solids. Lagrange multipliers are used on the fluid boundary to weakly enforce boundary conditions, which enables tracking free fluid surfaces and moving solid boundaries. The evolution of the discrete mesh in the fluid domain due to the motion of the solid and free surface is determined by the deformation of a fictitious structure. A fully implicit and an implicit-explicit scheme are used for the solution of monolithic and partitioned methods, respectively. We examine the performance and stability of these methods in two aspects: the motion of ultra-light solids that has been challenging to model computationally and the role of the numerical fluxes used for the viscous term. The latter relates this work to prior studies on the stability of various interior penalty and DG formulations for elliptic PDEs. Representative examples in both two and three dimensions show the capability to solve flows over moving and rotating objects.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114185"},"PeriodicalIF":3.8,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366663","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 review of low-rank methods for time-dependent kinetic simulations","authors":"Lukas Einkemmer ,&nbsp;Katharina Kormann ,&nbsp;Jonas Kusch ,&nbsp;Ryan G. McClarren ,&nbsp;Jing-Mei Qiu","doi":"10.1016/j.jcp.2025.114191","DOIUrl":"10.1016/j.jcp.2025.114191","url":null,"abstract":"<div><div>Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six–dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114191"},"PeriodicalIF":3.8,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501803","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":"Accurate calculation of bubble and droplet properties in diffuse-interface two-phase simulations","authors":"Pranav J. Nathan,&nbsp;Suhas S. Jain","doi":"10.1016/j.jcp.2025.114190","DOIUrl":"10.1016/j.jcp.2025.114190","url":null,"abstract":"<div><div>In this paper, we address the challenge of accurately calculating droplet/bubble properties (e.g., volume, number) in diffuse-interface two-phase flow simulations. Currently, flood-fill algorithms can truncate a significant portion of the volume of droplets/bubbles contained within the diffuse interface region or artificially merge multiple droplets/bubbles. This error is also dependent on the volume fraction cutoff value, which is typically chosen to be 0.5 arbitrarily, in the flood-fill algorithms. We propose a simple volume-correction approach that incorporates an analytical approximation of the truncated volume to correct for the missing droplet/bubble volumes. This proposed method results in accurately recovering the dispersed phase volumes with minimal volume error over a wide range of volume fraction cutoff values, and hence, can also accurately recover the number of droplets/bubbles. This can be a valuable tool for accurate calculation of drop/bubble size distributions for analysis and for Eulerian-to-Lagrangian conversion of the dispersed phase in multi-scale modeling approaches.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114190"},"PeriodicalIF":3.8,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366665","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":"Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations","authors":"Shumo Cui ,&nbsp;Yaguang Gu ,&nbsp;Alexander Kurganov ,&nbsp;Kailiang Wu ,&nbsp;Ruixiao Xin","doi":"10.1016/j.jcp.2025.114189","DOIUrl":"10.1016/j.jcp.2025.114189","url":null,"abstract":"<div><div>One major challenge in developing accurate and robust numerical schemes for compressible Euler equations arises due to the potential emergence of discontinuous structures in the solution. Recently proposed low-dissipation central-upwind (LDCU) schemes achieve sharp resolution of these structures without introducing spurious oscillations. However, unlike many other Godunov-type methods, the LDCU schemes cannot be written as a convex combination of first-order positivity-preserving (PP) schemes. Therefore, the PP property of the LDCU schemes cannot be analyzed by standard techniques. In this paper, we overcome this difficulty by first decomposing the studied schemes into a convex combination of several intermediate solution states, and then analyzing their PP properties. The performed analysis helps us to construct PPLDCU schemes for Euler equations of compressible gas dynamics, guaranteeing the positivity of computed density and pressure. To achieve the PP property, the built-in anti-diffusion terms in the two-dimensional case and the piecewise linear reconstruction procedure in both the one- and two-dimensional cases are redesigned. The effectiveness and robustness of the proposed PPLDCU schemes are demonstrated in several challenging numerical examples.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114189"},"PeriodicalIF":3.8,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489754","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":"On simple well-balanced semi-implicit and explicit numerical methods for blood flow in networks of elastic vessels with applications to FFR prediction","authors":"A. Lucca ,&nbsp;L.O. Müller ,&nbsp;L. Fraccarollo ,&nbsp;E.F. Toro ,&nbsp;M. Dumbser","doi":"10.1016/j.jcp.2025.114188","DOIUrl":"10.1016/j.jcp.2025.114188","url":null,"abstract":"<div><div>This paper proposes a semi-implicit 2D and a fully explicit 1D finite volume scheme for the simulation of blood flow in axially symmetric compliant vessels characterized by variable mechanical and geometrical parameters. The computational efficiency of the two methods are compared using patient-specific simulations designed to predict the haemodynamic impact of partial vessel occlusion in coronary trees.</div><div>The first method is a staggered semi-implicit one and solves a two-dimensional blood flow model with moving boundaries, derived from the Navier–Stokes equations in an axially symmetric geometry, by splitting it into two subsystems: one containing the nonlinear convective terms and a second subsystem for the pressure-related terms. An explicit approach is used for the nonlinear convective terms, while the pressure subsystem is treated implicitly. This leads to a CFL-type time step restriction which depends only on the bulk velocity of the flow and not on the speed of the pressure waves. The scheme is by construction well balanced for flow at rest and variable material parameters.</div><div>The second method is a novel fully explicit collocated path-free path-conservative finite volume scheme for simulating one-dimensional blood flow in networks of elastic vessels. The method is exactly well-balanced for flow at rest and general material parameters.</div><div>Both methodologies are then coupled to a simple 3D approach for the treatment of junctions where each junction is represented by a 3D cell and the Euler equations are employed to approximate the velocity and pressure unknowns. Thanks to a multidimensional numerical flux which takes into account the elementary information of the junction geometry, namely the normal vectors and areas of the incident vessels, the schemes are able to correctly capture the reflected waves, taking into account the effect of the different incident angles of the vessels at a junction.</div><div>The proposed methodologies are first validated using classical computational fluid dynamics benchmark tests and then applied to solve the flow dynamics in a network of multiple elastic arteries. In addition, to demonstrate the ability of the proposed methods to deal with a real clinical context, we study hemodynamics in patients affected by stable coronary artery disease, the pathological condition that occurs when an abnormal narrowing of the vessel wall is present. The capability of both methods to predict the Fractional Flow Reserve (FFR) index is shown and the results are compared with in vivo measurements and numerical estimates obtained with a 3D flow solver for a large number of patients.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114188"},"PeriodicalIF":3.8,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366664","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":"2D conservative sharp interface method for compressible three-phase flows: Ternary fluid flows and interaction of two-phase flows with solid","authors":"Zhu-Jun Li ,&nbsp;Yi Ren ,&nbsp;Yi Shen ,&nbsp;Hang Ding","doi":"10.1016/j.jcp.2025.114187","DOIUrl":"10.1016/j.jcp.2025.114187","url":null,"abstract":"<div><div>In this article, we propose a 2D conservative sharp interface method to simulate compressible three-phase flows that encompasses both ternary fluid flows and two-phase flows involving complex solid geometries. The evolution of the fluid-fluid interfaces and the geometry of the solid objects are tracked by a regional level-set function, and are repeatedly reconstructed on a background Cartesian mesh using line segments at each time step. To achieve a high resolution of the interfaces, we identify triple points where the ternary fluids meet or where the interface intersects with solid walls during the reconstruction process. Additionally, by exploiting the symmetry and rotational symmetry of fluid (and solid) positions within a cut cell (i.e., a Cartesian cell containing at least two phases), we reduce the configurations of the cut cells from 96 to 6 basic ones for two-dimensional simulations. Special treatment is also implemented for the cell assembly process in the vicinity of triple points. To ensure a unified approach to boundary conditions, we first identify the specific properties of the reconstructed interfaces, and subsequently enforce appropriate boundary conditions (i.e., jump conditions for interfaces and no-penetration conditions for solid walls) through the solution of a local 1D Riemann problem along the direction normal to the corresponding reconstructed interface. We employ a second-order finite volume method within the arbitrary Lagrange-Eulerian framework to discretize the Euler equations, thereby ensuring that the conservation of mass, momentum, and energy is maintained during the flow computation. The accuracy and robustness of the method are evaluated through numerous numerical experiments, including the compressible triple point problem, the interaction between a shock wave and a multi-medium bubble, high-speed droplet impingement on curved surfaces, and the water entry of a sphere at a uniform speed. The numerical results are validated against benchmark solutions available in the literature. Furthermore, the method is shown to effectively preserve the physical symmetry of ternary fluid flows, primarily due to the geometric resolution of the triple points and second-order accuracy in resolving interfaces.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114187"},"PeriodicalIF":3.8,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313085","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 matrix-free stabilized solver for the incompressible Navier-Stokes equations","authors":"Laura Prieto Saavedra ,&nbsp;Peter Munch ,&nbsp;Bruno Blais","doi":"10.1016/j.jcp.2025.114186","DOIUrl":"10.1016/j.jcp.2025.114186","url":null,"abstract":"<div><div>We present an efficient solver for the incompressible Navier-Stokes equations implemented in a matrix-free fashion. It uses a higher-order continuous Galerkin finite element method for the space discretization and leverages a stabilized formulation that includes both the SUPG and PSPG terms. We solve the non-linear problem in a fully coupled way, using a Newton-Krylov method, which is preconditioned by a monolithic geometric multigrid solver. To evaluate its efficiency in terms of time to solution and scalability on modern high-performance computers, we use a manufactured solution, a steady flow around a sphere with Reynolds number <span><math><mrow><mrow><mi>Re</mi></mrow><mo>=</mo><mn>150</mn></mrow></math></span> and the Taylor–Green vortex benchmark at <span><math><mrow><mrow><mi>Re</mi></mrow><mo>=</mo><mn>1</mn><mspace></mspace><mn>600</mn></mrow></math></span>. The results indicate that the solver is robust and scales for both steady-state and transient problems. We compare the matrix-free solver to a matrix-based version and show it exhibits lower memory requirements, better scalability, and significant speedups (10–100<span><math><mo>×</mo></math></span> for higher-order elements). Moreover, we demonstrate that a matrix-free implementation is highly efficient when using higher-order elements, which provide higher accuracy at a lower number of degrees of freedom for complex steady problems. To the best of our knowledge, this work is the first that uses a matrix-free monolithic geometric multigrid preconditioner to solve the stabilized Navier-Stokes equations. All implementations are available via the open-source software <span>Lethe</span>.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114186"},"PeriodicalIF":3.8,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321862","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":"FPINN-deeponet: A physics-informed operator learning framework for multi-term time-fractional mixed diffusion-wave equations","authors":"Binghang Lu ,&nbsp;ZhaoPeng Hao ,&nbsp;Christian Moya ,&nbsp;Guang Lin","doi":"10.1016/j.jcp.2025.114184","DOIUrl":"10.1016/j.jcp.2025.114184","url":null,"abstract":"<div><div>In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDWEs). We begin by deriving an <span><math><msub><mi>L</mi><mn>2</mn></msub></math></span> approximation, which achieves first-order accuracy for the Caputo fractional derivative of order <span><math><mrow><mi>β</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span>. Building upon this foundation, we propose the fPINN-DeepONet framework, a novel approach that integrates operator learning with the <span><math><msub><mi>L</mi><mn>2</mn></msub></math></span> approximation to efficiently solve fractional partial differential equations (FPDEs). Our framework is successfully applied to both fixed and variable fractional-order PDEs, demonstrating the framework’s versatility and broad applicability. To evaluate the performance of the proposed model, we conduct a series of numerical experiments that involve dynamically varying fractional orders in both space and time, as well as scenarios with noisy data. These results highlight the accuracy, robustness, and efficiency of the fPINN-DeepONet framework.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114184"},"PeriodicalIF":3.8,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306254","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":"Time-averaged algorithm for solving the topology optimization problem for unsteady laminar, turbulent and anisothermal flows","authors":"Delphine Ramalingom ,&nbsp;Alain Bastide ,&nbsp;Pierre-Henri Cocquet ,&nbsp;Michaël Rakotobé ,&nbsp;David Marti","doi":"10.1016/j.jcp.2025.114175","DOIUrl":"10.1016/j.jcp.2025.114175","url":null,"abstract":"<div><div>This paper proposes a new algorithm to solve topology optimization problems for laminar unsteady or turbulent flows. Instead of computing the gradient of the cost function after solving the direct and adjoint (both unsteady) PDE on the full time interval, our algorithm uses averaged physical quantities on a smaller unspecified time interval to define a (steady) Reynolds-Averaged Method (RAM) model which is then used as constraint in an optimization problem to update the design variable. Another feature of the proposed method is that the RAM model can be defined whatever the initial model and CFD turbulence models initially chosen to compute the instantaneous physical quantities. The RAM model involves turbulent quantities such as turbulent kinetic viscosity and turbulent thermal diffusivity are estimated instead of using the concept of ”frozen turbulence”. In contrast with the classical methods built to solve unsteady topology optimization problems, the main advantage of the proposed algorithm is that it updates the design variable by solving an auxiliary steady topology optimization problem. Three configuration cases are studied to illustrate the ability of our algorithm to optimize pressure losses and heat transfer by adding material to smooth the laminar unsteady or turbulent flows. We also calculate the number of required design parameter updates to obtain an optimized design. Thus, our algorithm overcomes three major scientific challenges in solving optimization problems in turbulence, namely leveraging efficient temporal turbulence models or a Direct Numerical Simulation (DNS) model, computational cost and data storage requirements.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114175"},"PeriodicalIF":3.8,"publicationDate":"2025-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280106","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 time marching scheme for solving compressible Navier–Stokes equations based on temporal reconstruction","authors":"Hanyu Zhou,&nbsp;Yu-xin Ren","doi":"10.1016/j.jcp.2025.114146","DOIUrl":"10.1016/j.jcp.2025.114146","url":null,"abstract":"<div><div>This paper presents a new family of high-order implicit time marching schemes based on direct integration and temporal reconstruction (DITR). These schemes can be used to solve the system of ordinary differential equations (ODEs) arising from semi-discretization of partial differential equations (PDEs) such as the compressible Navier–Stokes equations. DITR methods can be constructed with third- and fourth-order temporal accuracy in a straightforward fashion, and require fewer stages than some popular implicit Runge–Kutta schemes. Some DITR ODE integrators can achieve <span><math><mi>A</mi></math></span>-stability or <span><math><mi>L</mi></math></span>-stability. We present a matrix-free iteration method for solving the DITR equations, which ensures that DITR can be efficiently implemented in practical applications. The linear stability is realized by choosing an appropriate preconditioning parameter. The numerical results demonstrate that DITR methods can achieve high-order of accuracy with comparatively low computational cost. When achieving the same level of errors in numerical solutions, some DITR methods use significantly smaller amounts of time compared with the popular ESDIRK4 method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114146"},"PeriodicalIF":3.8,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144297162","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}