Journal of Computational Physics最新文献

{"title":"Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation","authors":"Steffen Schotthöfer ,&nbsp;M. Paul Laiu ,&nbsp;Martin Frank ,&nbsp;Cory D. Hauck","doi":"10.1016/j.jcp.2025.113967","DOIUrl":"10.1016/j.jcp.2025.113967","url":null,"abstract":"<div><div>The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub<span><span>¹</span></span>^,<span><span>²</span></span>.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113967"},"PeriodicalIF":3.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807380","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":"Non-conservative Godunov-type schemes: Application to two-phase flows with surface tension using Lagrange-transport splitting strategy","authors":"Lucas Tallois ,&nbsp;Simon Peluchon ,&nbsp;Gérard Gallice ,&nbsp;Philippe Villedieu","doi":"10.1016/j.jcp.2025.113958","DOIUrl":"10.1016/j.jcp.2025.113958","url":null,"abstract":"<div><div>This paper aims to present one-dimensional and multi-dimensional non-conservative Godunov-type schemes in a general framework. These schemes are designed to preserve equilibrium solutions discretely. Gallice's theory of simple solvers is used to solve the Riemann problem approximately. These numerical schemes are applied to compute two-phase flows with surface tension effects. Time integration is based on the Lagrange-Transport splitting strategy, allowing to solve the acoustic waves with an implicit time scheme.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113958"},"PeriodicalIF":3.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760396","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":"Robustness and efficiency of encapsulated selective frequency damping using different operator-splitting schemes: Application to laminar cylinder flow and transonic buffet","authors":"Lianyi Wei ,&nbsp;Guannan Zheng ,&nbsp;Xueyuan Nie ,&nbsp;Jinan Lv ,&nbsp;Chengde Huang ,&nbsp;Weishuang Lu ,&nbsp;Yuchen Zhang ,&nbsp;Guowei Yang","doi":"10.1016/j.jcp.2025.113968","DOIUrl":"10.1016/j.jcp.2025.113968","url":null,"abstract":"<div><div>A modified encapsulated selective frequency damping (MESFD) method based on the Strang splitting scheme is developed in this study. As a comparison the widely-used encapsulated form of selective frequency damping (ESFD) method constructed from the sequential splitting scheme is also introduced. Both methods are implemented into an implicit-time stepping Unsteady Navier-Stokes Equation (UNSE) solver and applied to solve the unstable steady solutions of the laminar cylinder flow and transonic buffet. It turns out that ESFD performs better than MESFD in convergence to the steady solution of the cylinder flow while MESFD does better in calculating the unstable steady solution of transonic buffet than ESFD. The traditional perspective of the global modes or the stability region fails to explain such discrepancies given that the same parameter combination of the control gain <span><math><mi>χ</mi></math></span> and the filtered width <span><math><mstyle><mi>Δ</mi></mstyle></math></span> is chosen in both methods. However, the viewpoint of local splitting errors established from the Lie operator formalism that relates the structure of the local splitting errors to the spatial accuracy and the parameter set <span><math><mrow><mo>(</mo><mrow><mi>χ</mi><mo>,</mo><mstyle><mi>Δ</mi></mstyle></mrow><mo>)</mo></mrow></math></span> gives new insights into the differences between MESFD and ESFD. How the local splitting errors contribute to the calculation and how to choose proper <span><math><mrow><mo>(</mo><mrow><mi>χ</mi><mo>,</mo><mstyle><mi>Δ</mi></mstyle></mrow><mo>)</mo></mrow></math></span> accordingly are discussed in these two flow problems. For the laminar cylinder flow problem, both ESFD and MESFD are independent of the mesh size. For the turbulent transonic buffet problem, although both ESFD and MESFD are highly sensitive to the mesh set up, MESFD is more robust and efficient for convergence to the unstable steady solution compared to ESFD.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113968"},"PeriodicalIF":3.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776474","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":"Regularity-conforming neural networks (ReCoNNs) for solving partial differential equations","authors":"Jamie M. Taylor ,&nbsp;David Pardo ,&nbsp;Judit Muñoz-Matute","doi":"10.1016/j.jcp.2025.113954","DOIUrl":"10.1016/j.jcp.2025.113954","url":null,"abstract":"<div><div>Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions –the natural function spaces for PDEs– by Neural Networks (NNs) of sufficient size, low-regularity solutions may lead to poor approximations in practice. For example, classical fully-connected feed-forward NNs fail to approximate continuous functions whose gradient is discontinuous when employing strong formulations like in Physics Informed Neural Networks (PINNs). In this article, we propose the use of regularity-conforming neural networks, where <em>a priori</em> information on the regularity of solutions to PDEs can be employed to construct proper architectures. We illustrate the potential of such architectures via a two-dimensional (2D) transmission problem, where the solution may admit discontinuities in the gradient across interfaces, as well as power-like singularities at certain points. In particular, we formulate the weak transmission problem in a PINNs-like strong formulation with interface and continuity conditions. Such architectures are partially explainable; discontinuities are explicitly described, allowing the introduction of novel terms into the loss function. We demonstrate via several model problems in one and two dimensions the advantages of using regularity-conforming architectures in contrast to classical architectures. The ideas presented in this article easily extend to problems in higher dimensions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113954"},"PeriodicalIF":3.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143745789","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":"FEM-MsFEM hybrid method for the Stokes-Darcy model","authors":"Yachen Hong ,&nbsp;Wenhan Zhang ,&nbsp;Lina Zhao ,&nbsp;Haibiao Zheng","doi":"10.1016/j.jcp.2025.113952","DOIUrl":"10.1016/j.jcp.2025.113952","url":null,"abstract":"<div><div>This paper explores the application of hybrid of the finite element method and multiscale finite element method (FEM-MsFEM) to address the steady-state Stokes-Darcy problems with Beavers-Joseph-Saffman (BJS) interface conditions in highly heterogeneous porous media. We propose an algorithm for this multiscale Stokes-Darcy model. The FEM-MsFEM hybrid method adapts to the characteristics of different regions. MsFEM basis functions are applied to the Darcy region, whereas standard finite element basis functions are utilized for the Stokes region. Afterward, the FEM-MsFEM basis functions are used for computations with the Robin-Robin domain decomposition algorithm. Furthermore, this special domain decomposition algorithm preserves a convergence rate independent of the mesh size. Subsequently, we conduct error analysis based on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms for this FEM-MsFEM hybrid method. Finally, we present extensive numerical tests, illustrating the results of error and convergence analysis.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113952"},"PeriodicalIF":3.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737973","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 reinterpreted discrete fracture model for wormhole propagation in fractured porous media","authors":"Xinyu Wu ,&nbsp;Hui Guo ,&nbsp;Ziyao Xu ,&nbsp;Lulu Tian ,&nbsp;Yang Yang","doi":"10.1016/j.jcp.2025.113953","DOIUrl":"10.1016/j.jcp.2025.113953","url":null,"abstract":"<div><div>Wormholes are high-permeability, deep-penetrating, narrow channels formed during the acidizing process, which serves as a popular stimulation treatment. For the study of wormhole formation in naturally fractured porous media, we develop a novel hybrid-dimensional two-scale continuum wormhole model, with fractures represented as Dirac-<em>δ</em> functions. As an extension of the reinterpreted discrete fracture model (RDFM) <span><span>[50]</span></span>, the model is applicable to nonconforming meshes and adaptive to intersecting fractures in reservoirs without introducing additional computational complexity. A numerical scheme based on the local discontinuous Galerkin (LDG) method is constructed for the corresponding dimensionless model to accommodate the presence of Dirac-<em>δ</em> functions and the property of flux discontinuity. Moreover, a bound-preserving technique is introduced to theoretically ensure the boundedness of acid concentration and porosity between 0 and 1, as well as the monotone increase in porosity during simulation. The performance of the model and algorithms is validated, and the effects of various parameters on wormhole propagation are analyzed through several numerical experiments, contributing to the acidizing design in fractured reservoirs.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113953"},"PeriodicalIF":3.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725289","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":"CGKN: A deep learning framework for modeling complex dynamical systems and efficient data assimilation","authors":"Chuanqi Chen ,&nbsp;Nan Chen ,&nbsp;Yinling Zhang ,&nbsp;Jin-Long Wu","doi":"10.1016/j.jcp.2025.113950","DOIUrl":"10.1016/j.jcp.2025.113950","url":null,"abstract":"<div><div>Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data assimilation (DA), which is a crucial technique for state estimation, model identification, and reconstructing missing data. Integrating ensemble-based DA methods with nonlinear deep learning models is computationally expensive and may suffer from large sampling errors. To address these challenges, we introduce a deep learning framework designed to simultaneously provide accurate forecasts and efficient DA. It is named Conditional Gaussian Koopman Network (CGKN), which transforms general nonlinear systems into nonlinear neural differential equations with conditional Gaussian structures. CGKN aims to retain essential nonlinear components while applying systematic and minimal simplifications to facilitate the development of analytic formulae for nonlinear DA. This allows for seamless integration of DA performance into the deep learning training process, eliminating the need for empirical tuning as required in ensemble methods. CGKN compensates for structural simplifications by lifting the dimension of the system, which is motivated by Koopman theory. Nevertheless, CGKN exploits special nonlinear dynamics within the lifted space. This enables the model to capture extreme events and strong non-Gaussian features in joint and marginal distributions with appropriate uncertainty quantification. We demonstrate the effectiveness of CGKN for both prediction and DA on three strongly nonlinear and non-Gaussian turbulent systems: the projected stochastic Burgers–Sivashinsky equation, the Lorenz 96 system, and the El Niño-Southern Oscillation. The results justify the robustness and computational efficiency of CGKN.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113950"},"PeriodicalIF":3.8,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738003","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":"Higher-order MPS models and higher-order Explicit Incompressible MPS (EI-MPS) method to simulate free-surface flows","authors":"Tibing Xu ,&nbsp;Seiichi Koshizuka ,&nbsp;Tsuyoshi Koyama ,&nbsp;Toshihide Saka ,&nbsp;Osamu Imazeki","doi":"10.1016/j.jcp.2025.113951","DOIUrl":"10.1016/j.jcp.2025.113951","url":null,"abstract":"<div><div>In this study, higher-order spatial models including the gradient model and Laplacian model based on Taylor's series and using their coordinates as coefficients are evaluated by calculating some simple functions and a diffusion problem. The numerical convergence is achieved by the models as the smaller particle distance can calculate more accurate results. By using the models, when the particle distribution is significantly irregular, increasing the search radius can involve more neighboring particles which consequently improves the accuracy. Based on the proposed higher-order models, the higher-order Explicit Incompressible version of the Moving Particle Semi-implicit method (EI-MPS) is developed. The numerical scheme is validated by simulating various free surface flows including the rotation of a fluid square patch, the impact of two identical rectangular fluid patches, oscillating drop under a central force field, a hydrostatic problem, and dam-break flow. The parameters of the particle distance, search radius, and repeated time in the pressure calculation are all examined in the free surface flows. The proposed method can reproduce the free surface variations, kinetic energy, and total energy variation in the violent flows. It can also obtain the hydrostatic pressure achieving numerical convergence. Increasing the search radius can result in larger errors in simulating the hydrostatic pressure. The impacting pressure caused by the dam-break flow is reflected by the method in good agreement with the experimental measurements.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113951"},"PeriodicalIF":3.8,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706232","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 thermodynamically consistent and conservative diffuse-interface model for gas/liquid-liquid-solid flows","authors":"Chengjie Zhan ,&nbsp;Xi Liu ,&nbsp;Zhenhua Chai ,&nbsp;Baochang Shi","doi":"10.1016/j.jcp.2025.113949","DOIUrl":"10.1016/j.jcp.2025.113949","url":null,"abstract":"<div><div>In this work, a thermodynamically consistent and conservative diffuse-interface model for gas/liquid-liquid-solid flows is proposed. In this model, a novel free energy for the gas/liquid-liquid-solid system is established according to a ternary phase-field model, and it not only contains the standard bulk and interface free energies for two-phase flows, but also includes some additional terms to reflect the penalty in the solid phase and the wettability on the solid surface. Furthermore, a smooth indicator function of the solid phase is also introduced in the consistent Navier-Stokes equations to achieve a high viscosity in the solid phase, and to preserve the velocity boundary conditions on the solid surface by the force caused by fluid-structure interaction. Based on the proposed diffuse-interface model, the fluid interface dynamics, the fluid-structure interaction, and the wetting property of the solid surface can be described simply and efficiently. Additionally, the total energy is also proved to be dissipative for the two-phase flows in the stationary geometries. To test the present diffuse-interface model, we develop a consistent and conservative lattice Boltzmann method and conduct some simulations. The numerical results also confirm the energy dissipation and good capability of the proposed diffuse-interface model in the study of two-phase flows in complex geometries and two-phase flows with moving particles.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113949"},"PeriodicalIF":3.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696117","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 efficient particle locating method on unstructured meshes in two and three dimensions based on patch searching","authors":"Shuang Chen ,&nbsp;Fanyi Yang","doi":"10.1016/j.jcp.2025.113948","DOIUrl":"10.1016/j.jcp.2025.113948","url":null,"abstract":"<div><div>We present a particle locating method for unstructured meshes in two and three dimensions. Our algorithm is based on a patch searching process, and includes two steps. We first locate the given point to a patch near a vertex, and then the host element is determined within the patch domain. Here, the patch near a vertex is the domain of elements around this vertex. We prove that in the first step the patch can be rapidly identified by constructing an auxiliary Cartesian grid with a prescribed resolution. Then, the second step can be converted into a searching problem, which can be easily solved by searching algorithms. Only coordinates to particles are required in our method. We conduct a series of numerical tests in two and three dimensions to illustrate the robustness and efficiency of our method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113948"},"PeriodicalIF":3.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686400","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}