Journal of Computational Physics最新文献

{"title":"Physics-informed neural networks for tsunami inundation modeling","authors":"Rüdiger Brecht ,&nbsp;Elsa Cardoso-Bihlo ,&nbsp;Alex Bihlo","doi":"10.1016/j.jcp.2025.114066","DOIUrl":"10.1016/j.jcp.2025.114066","url":null,"abstract":"<div><div>We use physics-informed neural networks for solving the shallow-water equations for tsunami modeling. Physics-informed neural networks are an optimization based approach for solving differential equations that is completely meshless. This substantially simplifies the modeling of the inundation process of tsunamis. While physics-informed neural networks require retraining for each particular new initial condition of the shallow-water equations, we also introduce the use of deep operator networks that can be trained to learn the solution operator instead of a particular solution only and thus provides substantial speed-ups, also compared to classical numerical approaches for tsunami models. We show with several classical benchmarks that our method can model both tsunami propagation and the inundation process exceptionally well.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114066"},"PeriodicalIF":3.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070788","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":"Hydrodynamic cavitation with non-condensable gases: A thickened interface method with differentiable non-equilibrium thermodynamics based on van der Waals theory","authors":"Saikat Mukherjee,&nbsp;Hector Gomez","doi":"10.1016/j.jcp.2025.114070","DOIUrl":"10.1016/j.jcp.2025.114070","url":null,"abstract":"<div><div>The van der Waals theory of phase transformations offers a fundamental framework for non-equilibrium thermodynamics of phase transforming fluids that can be coupled with flow using the Coleman-Noll procedure. Until recently, computations based on this modeling framework had been limited to very small length scales and low speed flows, but recent advances enable simulations at large Reynolds numbers and length scales. Here, we extend the van der Waals modeling framework and the enabling computational methods that were proposed for single-component fluids to a mixture of a phase-transforming fluid and a non-condensable gas. A key element of innovation in our approach is the development of an interface enlargement algorithm coupled with a stabilized numerical scheme that can robustly handle large density variations and remain stable in the non-hyperbolic region of the phase diagram. The accuracy, stability and robustness of the numerical method were verified through extensive numerical testing, including the use of theoretical and manufactured solutions as well as simulations of cavitating flow past a cylinder. Our simulations also show that the overall approach reproduces some of the experimental observations in cavitating flows with non-condensable gas in dissolution and in the form of nuclei, which underscores its potential to better predict and understand cavitating flows of mixtures.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114070"},"PeriodicalIF":3.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084459","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":"Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers","authors":"David Huergo ,&nbsp;Martín De Frutos ,&nbsp;Eduardo Jané ,&nbsp;Oscar A. Marino ,&nbsp;Gonzalo Rubio ,&nbsp;Esteban Ferrer","doi":"10.1016/j.jcp.2025.114080","DOIUrl":"10.1016/j.jcp.2025.114080","url":null,"abstract":"<div><div>We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop an offline training approach, decoupled from the main solver, which shows minimal overcost when performing simulations. In addition, we derive an inexpensive RL-based error estimation approach that enables the quantification of local discretization errors. The proposed methodology is agnostic to both the computational mesh and the partial differential equation to be solved.</div><div>The application of RL to mesh adaptation offers several benefits. It enables automated and adaptive mesh refinement, reducing the need for manual intervention. It optimizes computational resources by dynamically allocating high-order polynomials where necessary and minimizing refinement in stable regions. This leads to computational cost savings while maintaining the accuracy of the solution. Furthermore, RL allows for the exploration of unconventional mesh adaptations, potentially enhancing the accuracy and robustness of simulations. This work extends our original research in [1], offering a more robust, reproducible, and generalizable approach applicable to complex three-dimensional problems. We provide validation for laminar and turbulent cases: circular cylinders, Taylor Green Vortex and a 10MW wind turbine to illustrate the flexibility of the proposed approach.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114080"},"PeriodicalIF":3.8,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070789","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":"Nesterov acceleration for ensemble Kalman inversion and variants","authors":"Sydney Vernon ,&nbsp;Eviatar Bach ,&nbsp;Oliver R．A. Dunbar","doi":"10.1016/j.jcp.2025.114063","DOIUrl":"10.1016/j.jcp.2025.114063","url":null,"abstract":"<div><div>Ensemble Kalman inversion (EKI) is a derivative-free, particle-based optimization method for solving inverse problems. It can be shown that EKI approximates a gradient flow, which allows the application of methods for accelerating gradient descent. Here, we show that Nesterov acceleration is effective in speeding up the reduction of the EKI cost function on a variety of inverse problems. We also implement Nesterov acceleration for two EKI variants, unscented Kalman inversion and ensemble transform Kalman inversion. Our specific implementation takes the form of a particle-level nudge that is demonstrably simple to couple in a black-box fashion with any existing EKI variant algorithms, comes with no additional computational expense, and with no additional tuning hyperparameters. This work shows a pathway for future research to translate advances in gradient-based optimization into advances in gradient-free Kalman optimization.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"535 ","pages":"Article 114063"},"PeriodicalIF":3.8,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947837","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 moving mesh method for porous medium equation by the Onsager variational principle","authors":"Si Xiao ,&nbsp;Xianmin Xu","doi":"10.1016/j.jcp.2025.114061","DOIUrl":"10.1016/j.jcp.2025.114061","url":null,"abstract":"<div><div>In this paper, we present a novel moving mesh finite element method for solving the porous medium equation, using the Onsager variational principle as an approximation framework. We first demonstrate that a mixed formulation of the continuous problem can be derived by applying the Onsager principle. Subsequently, we develop several numerical schemes by approximating the problem within a nonlinear finite element space with free knots (movable nodes), following the same variational approach. We rigorously prove that the energy dissipation structure is preserved in both semi-discrete and fully implicit discrete schemes. Additionally, we propose a fully decoupled explicit scheme, which requires only the sequential solution of a few linear equations per time step. Other variants of the method can also be derived analogously to preserve mass conservation or to enhance stability. The numerical schemes achieve optimal convergence rates when the initial mesh is carefully chosen to ensure good approximation of the initial data. Through extensive numerical experiments, we evaluated and compared the efficiency and stability of the proposed schemes with existing approaches. For cases involving uniform initial meshes, all schemes exhibit good stability, with the fully decoupled scheme demonstrating superior computational efficiency. In contrast, when addressing singular problems on nonuniform meshes, the stabilized explicit scheme strikes a good balance between stability and computational efficiency. In addition, the method inherently captures the waiting time phenomenon without requiring user intervention, further illustrating its robustness.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114061"},"PeriodicalIF":3.8,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070786","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 moment-based Hermite WENO schemes for hyperbolic conservation laws on triangular meshes","authors":"Zhuang Zhao,&nbsp;Jianxian Qiu","doi":"10.1016/j.jcp.2025.114049","DOIUrl":"10.1016/j.jcp.2025.114049","url":null,"abstract":"<div><div>In this paper, we construct high-order Hermite weighted essentially non-oscillatory (HWENO) schemes for two-dimensional hyperbolic conservation laws on triangular meshes. These schemes integrate both zeroth- and first-order moments into spatial discretizations, yielding more compact stencils than same-order WENO schemes. Specifically, the third- and fifth-order HWENO schemes require only one and two layers of stencils, respectively, as opposed to the two layers needed by a third-order WENO scheme. Meanwhile, the HWENO schemes demonstrate reduced numerical errors in smooth areas and improved resolutions near discontinuities. Although the HWENO schemes include two auxiliary equations, they retain a unified nonlinear reconstruction process similar to that of WENO schemes. This design choice leads to a modest increase in computational expense and algorithm complexity. Crucially, an efficient definition of smoothness indicators is introduced, based on a midpoint numerical integration of the original definition. This streamlined definition enhances computational efficiencies on unstructured meshes and results in only minor variations in smoothness measurement between the two definitions, regardless of whether the problem is smooth or discontinuous. The HWENO schemes are distinguished by their strong practicality on triangular meshes, with efficient computation of smoothness indicators, consistent use of a single set of compact stencils, and application of artificial linear weights. Extensive numerical experiments are conducted to verify the high-order accuracies, efficiencies, resolutions, robustness, scale-invariance, and the effectiveness of the smoothness indicator for the proposed HWENO schemes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"535 ","pages":"Article 114049"},"PeriodicalIF":3.8,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143924698","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":"Sharp front tracking with geometric interface reconstruction","authors":"Christian Gorges ,&nbsp;Fabien Evrard ,&nbsp;Robert Chiodi ,&nbsp;Berend van Wachem ,&nbsp;Fabian Denner","doi":"10.1016/j.jcp.2025.114059","DOIUrl":"10.1016/j.jcp.2025.114059","url":null,"abstract":"<div><div>This paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"535 ","pages":"Article 114059"},"PeriodicalIF":3.8,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947691","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":"Enhanced profile-preserving phase-field model of two-phase flow with surfactant interfacial transport and Marangoni effects","authors":"Haohao Hao,&nbsp;Xiangwei Li,&nbsp;Tian Liu,&nbsp;Huanshu Tan","doi":"10.1016/j.jcp.2025.114058","DOIUrl":"10.1016/j.jcp.2025.114058","url":null,"abstract":"<div><div>Using a regularized delta function to distribute surfactant interfacial concentration can simplify the computation of the surface gradient operator <span><math><msub><mi>∇</mi><mi>s</mi></msub></math></span>, enabling the phase-field model to effectively simulate Marangoni flows involving surfactant transport. However, the exact conservation of total surfactant mass is compromised due to deviation from the equilibrium phase field profile, numerical diffusion, and mass non-conservation in each phase. To overcome these limitations, we have developed a new model for simulating two-phase flow with surfactant transport along the interface. This model employs a profile-preserving strategy to maintain the equilibrium interface profile, ensuring accurate calculation of the regularized delta function and improving surfactant mass conservation. Within the framework of the advective Cahn-Hilliard phase-field model, we utilize a regularized delta function with a reduced gradient to minimize numerical diffusion. Furthermore, we introduce a hybrid surface tension model that integrates the free-energy and the continuum-surface force models to mitigate spatial discretization errors, particularly in scenarios with high density and viscosity ratios. Verification tests demonstrate the model’s effectiveness in simulating surface diffusion on stationary and expanding drops, suppressing spurious currents, and capturing the deformation of a two-dimensional drop in shear flow. The results closely align with analytical solutions and previous numerical studies. Finally, we apply the model to investigate the contraction and oscillation dynamics of a surfactant-laden liquid filament, revealing the role of the Marangoni force in shaping filament behavior.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114058"},"PeriodicalIF":3.8,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068171","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 score-based particle method for homogeneous Landau equation","authors":"Yan Huang,&nbsp;Li Wang","doi":"10.1016/j.jcp.2025.114053","DOIUrl":"10.1016/j.jcp.2025.114053","url":null,"abstract":"<div><div>We propose a novel score-based particle method for solving the Landau equation in plasmas, which seamlessly integrates learning with structure-preserving particle methods [1]. Building upon the Lagrangian viewpoint of the Landau equation, a central challenge stems from the nonlinear dependence of the velocity field on the density. Our primary innovation lies in recognizing that this nonlinearity is in the form of the score function, which can be approximated dynamically via techniques from score-matching. The resulting method inherits the conservation properties of the deterministic particle method while sidestepping the necessity for kernel density estimation in [1]. This streamlines computation and enhances scalability with dimensionality. Furthermore, we provide a theoretical estimate by demonstrating that the KL divergence between our approximation and the true solution can be effectively controlled by the score-matching loss. Additionally, by adopting the flow map viewpoint, we derive an update formula for exact density computation. Extensive examples have been provided to show the efficiency of the method, including a physically relevant case of Coulomb interaction.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114053"},"PeriodicalIF":3.8,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084460","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 multi-mesh approach for accurate computation of multi-target functionals in aerodynamics design","authors":"Guanghui Hu ,&nbsp;Ruo Li ,&nbsp;Jingfeng Wang","doi":"10.1016/j.jcp.2025.114054","DOIUrl":"10.1016/j.jcp.2025.114054","url":null,"abstract":"<div><div>Aerodynamic optimal design is crucial for enhancing performance of aircrafts, while calculating multi-target functionals through solving dual equations with arbitrary right-hand sides remains challenging. In this paper, a novel multi-target framework of DWR-based mesh refinement is proposed and analyzed. Theoretically, an extrapolation method is generalized to expand multi-variable functionals, which guarantees that the dual equations of different objective functionals can be calculated separately. Numerically, an algorithm of calculating multi-target functionals is designed based on the multi-mesh approach, which can help to obtain different dual solutions simultaneously. One feature of our framework is that the algorithm is easy to implement with the help of the hierarchical geometry tree structure and the calculation avoids the Galerkin orthogonality naturally. The framework takes a balance between different targets even when they are not the same orders of magnitude. While existing approach uses a linear combination of different components in multi-target functionals for adaptation, it introduces additional coefficients for adjusting. With each component calculated under a dual-consistent scheme, this multi-mesh framework addresses challenges such as the lift-drag ratio and other kinds of multi-target functionals, ensuring smooth convergence and precise calculations of dual solutions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"535 ","pages":"Article 114054"},"PeriodicalIF":3.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947692","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}