{"title":"The decomposed HOLO scheme: Enabling large time steps for the gray radiative transfer equation across three distinct limits","authors":"Zhiyi Feng , Tao Xiong , Min Tang","doi":"10.1016/j.jcp.2025.114092","DOIUrl":"10.1016/j.jcp.2025.114092","url":null,"abstract":"<div><div>In this paper, we introduce an asymptotic preserving Decomposed HOLO scheme for solving the gray radiative transfer equation under various scalings. We consider three distinct multiscale parameter regimes: the diffusive regime, the steady state regime, and the free-streaming regime. We decompose the light intensity into three components: the zeroth and first order moments, and a residual part. A Low-Order (LO) nonlinear macroscopic system is solved for the first two moments and the material temperature. The High-Order (HO) system targets the residual component instead of the light intensity in the HOLO algorithm found in the literature. This novel decomposed HOLO system facilitates the analytical proof of the asymptotic preserving properties in three different parameter regimes and eases the achievement of consistency between the HO and LO systems at the discrete level. To bolster stability, in the LO system, we use the characteristic method to provide a predication of the contributions from HO system. Numerical examples demonstrate that our scheme allows for large time steps, comparable to those in fully implicit schemes and independent of the speed of light. Various tests for accuracy and stability across different parameter regimes are presented, including benchmark tests such as the Marshak wave and Hohlraum problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114092"},"PeriodicalIF":3.8,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185241","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}
Vasiliy A. Es’kin , Alexey O. Malkhanov , Mikhail E. Smorkalov
{"title":"Are two hidden layers still enough for the physics-informed neural networks?","authors":"Vasiliy A. Es’kin , Alexey O. Malkhanov , Mikhail E. Smorkalov","doi":"10.1016/j.jcp.2025.114085","DOIUrl":"10.1016/j.jcp.2025.114085","url":null,"abstract":"<div><div>The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks with a single hidden layer to solve physical problems described by ordinary differential equations (ODEs) and partial differential equations (PDEs). A method for strictly deterministic initialization of a neural network with one hidden layer for solving physical problems described by an ODE is proposed. Modifications to existing methods for weighting the loss function (<span><math><mi>δ</mi></math></span>-causal training and gradient normalization) are given, as well as new methods developed for training strictly deterministic-initialized neural networks to solve ODEs (detaching, additional weighting based on the second derivative, predicted solution-based weighting, relative residuals). An algorithm for physics-informed data-driven initialization of a neural network with one hidden layer is proposed. A neural network with pronounced generalizing properties is presented, meaning that for unseen problem parameters it delivers the solution accuracy close to that of parameters seen in the training dataset. The generalizing abilities of such neural network can be precisely controlled by adjusting the neural network parameters. A metric for measuring the generalization of such neural network has been introduced. A gradient-free neuron-by-neuron (NbN) fitting method has been developed for adjusting the parameters of a single-hidden-layer neural network, which does not require the use of an optimizer or solver for its implementation. The proposed methods have been extended to 2D problems using the separable physics-informed neural networks (SPINN) approach. Numerous experiments have been carried out to develop the above methods and approaches. Experiments on physical problems, such as solving various ODEs and PDEs, have demonstrated that these methods for initializing and training neural networks with one or two hidden layers (SPINN) achieve competitive accuracy and, in some cases, state-of-the-art results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114085"},"PeriodicalIF":3.8,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144139796","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":"Optimization-based model order reduction of fluid-structure interaction problems","authors":"Tommaso Taddei , Xuejun Xu , Lei Zhang","doi":"10.1016/j.jcp.2025.114084","DOIUrl":"10.1016/j.jcp.2025.114084","url":null,"abstract":"<div><div>We introduce optimization-based full-order and reduced-order formulations of fluid-structure interaction problems. We study the flow of an incompressible Newtonian fluid which interacts with an elastic body: we consider an arbitrary Lagrangian Eulerian formulation of the fluid problem and a fully Lagrangian formulation of the solid problem; we rely on a finite element discretization of both fluid and solid equations. The distinctive feature of our approach is an implicit coupling of fluid and structural problems that relies on the solution to a constrained optimization problem with equality constraints. We discuss the application of projection-based model reduction to both fluid and solid subproblems: we rely on Galerkin projection for the solid equations and on least-squares Petrov-Galerkin projection for the fluid equations. Numerical results for three model problems illustrate the many features of the formulation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114084"},"PeriodicalIF":3.8,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090141","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 WCSPH-MSDEM model for combined rolling and sliding motions of complex-shaped blocks in an unsteady flow","authors":"Sen Gao , Bing Ren , Pengzhi Lin , Ping Dong","doi":"10.1016/j.jcp.2025.114083","DOIUrl":"10.1016/j.jcp.2025.114083","url":null,"abstract":"<div><div>A coupled Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) and Multi-Sphere Discrete Element Method (MSDEM) numerical model is employed to investigate the interaction between a discrete, complex-shaped block and a solid boundary in unsteady flows. The study focuses on enhancing the original MSDEM by developing a virtual surface algorithm that assigns a surface normal vector and a virtual surface to each boundary sphere, thereby allowing for a more accurate representation of the true boundary geometry. This approach ensures a precise description of normal contact between the block and the boundary while preventing the embedding phenomenon during the block’s sliding motion. To accurately simulate frictional behavior, both static friction theory and Coulomb’s law of kinetic friction are incorporated. A series of test cases are conducted to validate the modified MSDEM, with further validation of the coupled WCSPH-MSDEM model against experimental data concerning with the sliding motion of a hollow square under solitary waves. Finally, a numerical case study on combined rolling, sliding, and collision of a hollow square on a slope under plunging waves is presented, highlighting the stability and robustness of the proposed model.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114083"},"PeriodicalIF":3.8,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090140","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":"Physics-informed neural networks for tsunami inundation modeling","authors":"Rüdiger Brecht , Elsa Cardoso-Bihlo , 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":"An anisotropic nonlinear stabilization for finite element approximation of Vlasov–Poisson equations","authors":"Junjie Wen, Murtazo Nazarov","doi":"10.1016/j.jcp.2025.114079","DOIUrl":"10.1016/j.jcp.2025.114079","url":null,"abstract":"<div><div>We introduce a high-order finite element method for approximating the Vlasov–Poisson equations. This approach employs continuous Lagrange polynomials in space and explicit Runge–Kutta schemes for time discretization. To stabilize the numerical oscillations inherent in the scheme, a new anisotropic nonlinear artificial viscosity method is introduced. Numerical results demonstrate that this method achieves optimal convergence order with respect to both the polynomial space and time integration. The method is validated using classic benchmark problems for the Vlasov–Poisson equations, including Landau damping, two-stream instability, and bump-on-tail instability in a two-dimensional phase space.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114079"},"PeriodicalIF":3.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090138","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 bound-preserving Runge–Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws","authors":"Chen Liu , Zheng Sun , Xiangxiong Zhang","doi":"10.1016/j.jcp.2025.114071","DOIUrl":"10.1016/j.jcp.2025.114071","url":null,"abstract":"<div><div>In this paper, we develop bound-preserving techniques for the Runge–Kutta (RK) discontinuous Galerkin (DG) method with compact stencils (cRKDG method) for hyperbolic conservation laws. The cRKDG method was recently introduced in [Q. Chen, Z. Sun, and Y. Xing, <em>SIAM J. Sci. Comput.</em>, 46: A1327–A1351, 2024]. It enhances the compactness of the standard RKDG method, resulting in reduced data communication, simplified boundary treatments, and improved suitability for local time marching. This work improves the robustness of the cRKDG method by enforcing desirable physical bounds while preserving its compactness, local conservation, and high-order accuracy. Our method is extended from the seminal work of [X. Zhang and C.-W. Shu, <em>J. Comput. Phys.</em>, 229: 3091–3120, 2010]. We prove that the cell average of the cRKDG method at each RK stage preserves the physical bounds by expressing it as a convex combination of three types of forward-Euler solutions. A scaling limiter is then applied after each RK stage to enforce pointwise bounds. Additionally, we explore RK methods with less restrictive time step sizes. Because the cRKDG method does not rely on strong-stability-preserving RK time discretization, it avoids its order barriers, allowing us to construct a four-stage, fourth-order bound-preserving cRKDG method. Numerical tests on challenging benchmarks are provided to demonstrate the performance of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114071"},"PeriodicalIF":3.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116070","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, 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":"An adaptive manifold- and discrete empirical interpolation method-based reduced order model for nonlinear solids","authors":"Zachariah El-Hajj, Karel Matouš","doi":"10.1016/j.jcp.2025.114069","DOIUrl":"10.1016/j.jcp.2025.114069","url":null,"abstract":"<div><div>Predicting the multiscale nonlinear behavior of heterogeneous materials is critical to many engineering fields but requires computationally intensive techniques such as Computational Homogenization (CH). Reduced Order Model (ROM) surrogates have been developed to address the demands of multiscale modeling, but most are limited to single-scale or linear behavior. To this end, we propose a novel form of ROM that bypasses the associated computational requirements of scale and nonlinearity. The ROM is constructed within a CH framework and reduces irreversible processes at the fine scale. Reduction of Partial Differential Equations (PDEs) for geometric nonlinearities is accomplished using a Manifold-based Nonlinear Reduced Order Model (MNROM) which can interpolate microscopic fields from principal components. Reduction of Ordinary Differential Equations (ODEs) for material nonlinearities is accomplished using the Adaptive Discrete Empirical Interpolation Method (ADEIM) with adaptive sampling, which can project evolving field data globally from a few locally modeled points. Both PDE and ODE schemes are joined together using operator splitting and scale transition relationships to tackle coupled problems. We demonstrate the coupled ROM by examining elastoviscoplastic behavior in a particulate composite with a nearly incompressible binder. This is done for a complex 2D microstructure over a large range of strains and plastic deformations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114069"},"PeriodicalIF":3.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167109","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 tractable nonparametric probabilistic approach for modeling and quantifying model-form uncertainty in turbulent CFD","authors":"Emily Jewell , Charbel Farhat , Christian Soize","doi":"10.1016/j.jcp.2025.114067","DOIUrl":"10.1016/j.jcp.2025.114067","url":null,"abstract":"<div><div>This paper presents an innovative, computationally tractable approach for modeling and quantifying model-form uncertainty (MFU) in viscous computational fluid dynamics (CFD) models. It distinguishes between two sources of uncertainty: those related to turbulence modeling and other sources such as wall and far-field boundary conditions. The proposed approach comprises two complementary and coupled methods for uncertainty quantification (UQ): one targeting uncertainties in Reynolds stress modeling; and the other addressing all remaining model-form and parametric uncertainties. The first method decomposes the Reynolds stress tensor into a trace-vanishing deviatoric component and a spherical part. It then constructs a hyperparameterized probability model for the eigenvalues of the deviatoric component, based on its spectral algebraic properties. Further probabilistic modeling yields a complete hyperparameterized model for the Reynolds stress tensor, with each realization corresponding to an admissible turbulence model within a specific family. The second method adapts a recently developed nonparametric probabilistic approach for modeling and quantifying MFU to the context of this study. It relies on a probabilistic, projection-based model order reduction (PMOR) technique that is also hyperparameterized, ensuring computational tractability for UQ. The hyperparameters for both methods are simultaneously determined by formulating and minimizing an appropriate data-driven probabilistic loss function. Additionally, the methodology accounts for the uncertainties associated with PMOR, which is introduced to achieve efficient Monte Carlo simulations. The efficacy of the overall approach proposed for UQ in large-scale CFD computations is demonstrated through the Reynolds-averaged Navier-Stokes-based aerodynamic analysis of a rigid NASA Common Research Model configuration in the transonic flow regime, for which wind tunnel data is available.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114067"},"PeriodicalIF":3.8,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107019","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}