Journal of Computational Physics最新文献

{"title":"Toward accurate and efficient multi-moment finite volume method for large eddy simulations of compressible flows on unstructured grids","authors":"Ying Yang ,&nbsp;Feng Xiao ,&nbsp;Bin Xie","doi":"10.1016/j.jcp.2026.114668","DOIUrl":"10.1016/j.jcp.2026.114668","url":null,"abstract":"<div><div>A novel multi-moment finite volume method is proposed for the solutions of linear and nonlinear hyperbolic equations on unstructured grids and further investigated for implicit large eddy simulation of compressible turbulence. Different from the previous volume integrated average and point value based multi-moment (VPM) method, the present scheme first reconstructs the solution values and first-order derivatives at boundary surfaces and then constructs a quadratic polynomial over each cell using Gauss divergence theorem. It eliminates the need to directly compute second derivatives of solution variables, which is more efficient than conventional finite volume discretizations at third-order accuracy. The so-called VPM-FR (VPM with face-based reconstruction) formulates novel spatial reconstruction within a compact stencil consisting of only face neighbouring cells, which substantially improves the numerical accuracy, efficiency, robustness as well as algorithmic simplicity. Fourier analysis is also conducted to verify the numerical properties of VPM-FR which are compared against the previous version of VPM scheme. Besides, a new limiting projection approach is devised to use a high-order limiter function which effectively suppresses the numerical oscillation in the vicinity of discontinuities. Numerical results of various benchmark tests are presented for the advection, Euler and Navier-Stokes equations which validate the excellent performance of VPM-FR scheme that well resolves broadband turbulence and the sharp shock profiles with a reduction in computation cost.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114668"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957737","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":"Enabling probabilistic learning on manifolds through double diffusion maps","authors":"Dimitris G. Giovanis ,&nbsp;Nikolaos Evangelou ,&nbsp;Ioannis G. Kevrekidis ,&nbsp;Roger G. Ghanem","doi":"10.1016/j.jcp.2026.114663","DOIUrl":"10.1016/j.jcp.2026.114663","url":null,"abstract":"<div><div>We present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114663"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975678","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":"R-PINN: Recovery-type a-posteriori estimator enhanced adaptive PINN","authors":"Rongxin Lu ,&nbsp;Jiwei Jia ,&nbsp;Young Ju Lee ,&nbsp;Zheng Lu ,&nbsp;Chen-Song Zhang","doi":"10.1016/j.jcp.2026.114684","DOIUrl":"10.1016/j.jcp.2026.114684","url":null,"abstract":"<div><div>In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide range of equations, they often exhibit a suboptimal performance when applied to equations with large local gradients, resulting in substantially localized errors. To address this issue, this paper proposes an adaptive PINN algorithm designed to improve accuracy in such cases. The core idea of the algorithm is to adaptively adjust the distribution of collocation points based on the recovery-type a-posteriori error of the current numerical solution, enabling a better approximation of the true solution. This approach is inspired by the adaptive finite element method. By combining the recovery-type a-posteriori estimator, a gradient-recovery estimator commonly used in the adaptive finite element method (FEM), with PINNs, we introduce the recovery-type a-posteriori estimator enhanced adaptive PINN (R-PINN) and compare its performance with a typical adaptive sampling PINN, failure-informed PINN (FI-PINN), and a typical adaptive weighting PINN, residual-based attention in PINN (RBA-PINN) as a baseline. Our results demonstrate that R-PINN achieves faster convergence with fewer adaptively distributed points and outperforms the other two PINNs in the cases with regions of large errors.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114684"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035681","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":"Differentiable neural network representation of multi-well, locally-convex potentials","authors":"Reese E. Jones ,&nbsp;Adrian Buganza Tepole ,&nbsp;Jan N. Fuhg","doi":"10.1016/j.jcp.2026.114688","DOIUrl":"10.1016/j.jcp.2026.114688","url":null,"abstract":"<div><div>Multi-well potentials are ubiquitous in science, modeling phenomena such as phase transitions, dynamic instabilities, and multimodal behavior across physics, chemistry, and biology. In contrast to non-smooth minimum-of-mixture representations, we propose a differentiable and convex formulation based on a log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes. This log-sum-exponential input convex neural network (LSE-ICNN) provides a smooth surrogate that retains convexity within basins and allows for gradient-based learning and inference.</div><div>A key feature of the LSE-ICNN is its ability to automatically discover both the number of modes and the scale of transitions through sparse regression, enabling adaptive and parsimonious modeling. We demonstrate the versatility of the LSE-ICNN across diverse domains, including mechanochemical phase transformations, microstructural elastic instabilities, conservative biological gene circuits, and variational inference for multimodal probability distributions. These examples highlight the effectiveness of the LSE-ICNN in capturing complex multimodal landscapes while preserving differentiability, making it broadly applicable in data-driven modeling, optimization, and physical simulation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114688"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975680","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":"Investigation of new analytical and numerical solutions of the extended (2+1) dimensional Boussinesq equation using fractional derivative approaches","authors":"İlknur Kızıl ,&nbsp;Ulviye Demirbilek ,&nbsp;Ercan Çelik","doi":"10.1016/j.jcp.2026.114654","DOIUrl":"10.1016/j.jcp.2026.114654","url":null,"abstract":"<div><div>This study investigates the new fractional (2+1)-dimensional, extended Boussinesq (eBO) equation, which models the behavior of shallow water waves in channels with constant depth and flow velocity. This equation holds considerable relevance in fields such as ocean engineering, coastal hydrodynamics, plasma physics, and nonlinear wave theory. By applying the <span><math><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>/</mo><msup><mi>G</mi><mo>′</mo></msup><mo>)</mo></mrow></math></span>–expansion method, the sub-equation method, and dummyTXdummy– the modified extended tanh function method within the framework of conformable derivatives, a wide array of analytical traveling wave solutions is obtained. These include dark, bright, periodic, singular, exponential, and generalized hyperbolic-type solitons with kink-like features. The fractional transformation technique transforms the original fractional partial differential equations into ordinary differential equations, thereby simplifying the solution process. Moreover, the residual power series method (RPSM) is employed to approximate the solution of this equation, and modulation instability (MI) analysis is conducted to evaluate the stability of the obtained analytical solutions. The study includes comparison tables and various graphical representations to validate the solutions. The numerical findings demonstrate that all methods effectively provide exact and approximate solutions to nonlinear fractional differential equations. The temporal progression and spatial features of the solutions are visualized through 2D, 3D, and contour plots with a comparison of different fractional values. Computational validations are conducted using software, demonstrating the efficiency and general applicability of the proposed approach.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114654"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975682","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 implicit shock tracking method for simulation of shock-dominated flows over complex domains using mesh-based parametrizations","authors":"Alexander M. Pérez Reyes,&nbsp;Matthew J. Zahr","doi":"10.1016/j.jcp.2025.114647","DOIUrl":"10.1016/j.jcp.2025.114647","url":null,"abstract":"<div><div>A mesh-based parametrization is a parametrization of a geometric object that is defined solely from a mesh of the object, e.g., without an analytical expression or computer-aided design (CAD) representation of the object. In this work, we propose a mesh-based parametrization of an arbitrary <em>d</em>′-dimensional object embedded in a <em>d</em>-dimensional space using tools from high-order finite elements. Using mesh-based parametrizations, we construct a boundary-preserving parametrization of the nodal coordinates of a computational mesh that ensures all nodes remain on all their original boundaries. These boundary-preseving parametrizations allow the nodes of the mesh to move only in ways that will not change the computational domain. They also ensure nodes will not move between boundaries, which would cause issues assigning boundary conditions for partial differential equation simulations and lead to inaccurate geometry representations for non-smooth boundary transitions. Finally, we integrate boundary-preserving, mesh-based parametrizations into high-order implicit shock tracking, an optimization-based discontinuous Galerkin method that moves nodes to align mesh faces with non-smooth flow features to represent them perfectly with inter-element jumps, leaving the intra-element polynomial basis to represent smooth regions of the flow with high-order accuracy. Mesh-based parametrizations enable implicit shock tracking simulations of shock-dominated flows over geometries without simple analytical parametrizations. Several demonstrations of mesh-based parametrizations are provided to: (1) give concrete examples of the formulation, (2) show that accurate parametrizations can be obtained despite the surrogate surfaces only being <em>C</em>⁰, (3) show they integrate seemlessly with implicit shock tracking and can be used to parametrize surfaces without explicit expressions, and (4) effectively parametrize complex geometries and prevent nodes from moving off their original boundaries.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114647"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975681","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":"Polynomial range estimation as a troubled-cell indicator for high-order methods","authors":"Madeline M. Peck,&nbsp;Jiajia Waters","doi":"10.1016/j.jcp.2026.114687","DOIUrl":"10.1016/j.jcp.2026.114687","url":null,"abstract":"<div><div>Two troubled-cell indicators based on polynomial range estimation methods are used to flag cells that may violate positivity constraints. One method uses interval extension, and the second uses the range enclosure property of the Bernstein polynomial basis. Both methods reduce compute time for the positivity preserver by limiting its application to a subset of cells. The Bernstein polynomial method remains effective as the problem dimensionality increases. Interval extension applied to the internal energy equation permits the use of the troubled-cell indicators for rational functions, though performance suffers compared to directly applying the indicators to polynomial functions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114687"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035679","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":"Three-dimensional soft discrete element method for large-scale simulations of soft spheres","authors":"Zonglin Li ,&nbsp;Ju Chen ,&nbsp;Qiang Tian ,&nbsp;Haiyan Hu","doi":"10.1016/j.jcp.2026.114681","DOIUrl":"10.1016/j.jcp.2026.114681","url":null,"abstract":"<div><div>Soft particles are ubiquitous in both nature and industries, yet existing three-dimensional simulation methods remain inefficient. This paper presents a three-dimensional soft discrete element method (3D SDEM) for the efficient large-scale dynamic simulations of soft spherical particles. In the method, each soft sphere is modeled as a truncated ellipsoid with a homogeneous strain field, which requires 12 degrees of freedom only. The dynamic equations of soft spheres are derived by using the Lagrange-d’Alembert principle, and the contact detection between soft spheres is handled via the Common Normal Method. The contact force model and the strain energy function are formulated and validated through various compression scenarios of a single soft sphere. The accuracy and efficiency of the 3D SDEM are verified through two-sphere collision simulations and three-dimensional soft sphere compaction simulations. Notably, the compression of 10,000 soft spheres from a jammed state to 95 % volume fraction is simulated within five hours on a laptop computer with a single GPU only. Finally, the method is used to simulate the shear flow of soft particle glasses comprising 1000 soft spheres and successfully capture individual soft sphere deformations not reported before. These results demonstrate that the 3D SDEM enables the efficient modeling of large-scale soft sphere systems, paving the way for advanced studies in both physics and engineering applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114681"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035639","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":"Linear high order finite difference methods with essentially non-oscillatory limiters for hyperbolic conservation laws","authors":"Zhengfu Xu","doi":"10.1016/j.jcp.2026.114686","DOIUrl":"10.1016/j.jcp.2026.114686","url":null,"abstract":"<div><div>For high order finite difference and finite volume methods solving hyperbolic conservation laws, the major challenge is to achieve nonlinear stability in the presence of discontinuous solutions. Total variation diminishing or total variation bounded flux limiters are normally set up to achieve the nonlinear stability. High order essentially non-oscillatory methods (ENO or weighted ENO) were designed to avoid constructing high order polynomials across discontinuities to ensure nonlinear stability. However, adaptively reconstructing high order polynomials and doing so in the characteristic space often contributes significantly to the overall computational cost.</div><div>Alternatives were proposed as hybrid approaches: simply put, applying limiters in the discontinuous regions of the solution while using linear high order methods in the smooth regions. The key to the success of the hybrid approach lies in the differentiation between smooth and nonsmooth regions, which is highly nontrivial given discrete data sets. In this paper, an irregularity detecting mechanism is provided along the discrete profile of the solution to determine when the nonlinear ENO or WENO methods are needed. The irregularity detector does not depend on manually adjusted parameters when problems change. Such an irregularity detector is easy to implement in the dimensional splitting setting of the finite difference methods. The numerical evidences demonstrate the performance of the newly defined irregularity detector. When applied to high order finite difference methods, the numerical results are accurate and non-oscillatory with improved efficiency.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114686"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035641","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":"BiLO: Bilevel Local Operator Learning for PDE Inverse Problems","authors":"Ray Zirui Zhang ,&nbsp;Christopher E. Miles ,&nbsp;Xiaohui Xie ,&nbsp;John S. Lowengrub","doi":"10.1016/j.jcp.2026.114679","DOIUrl":"10.1016/j.jcp.2026.114679","url":null,"abstract":"<div><div>We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to locally approximate the PDE solution operator in the neighborhood of a given set of PDE parameters, which enables an accurate approximation of the descent direction for the upper level optimization problem. The lower level loss function includes the least-square penalty of both the residual and its derivative with respect to the PDE parameters. We apply gradient descent simultaneously on both the upper and lower level optimization problems, leading to an effective and fast algorithm. The method, which we refer to as BiLO (Bilevel Local Operator learning), is also able to efficiently infer unknown functions in the PDEs through the introduction of an auxiliary variable. We provide a theoretical analysis that justifies our approach. Through extensive experiments over multiple PDE systems, we demonstrate that our method enforces strong PDE constraints, is robust to sparse and noisy data, and eliminates the need to balance the residual and the data loss, which is inherent to the soft PDE constraints in many existing methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114679"},"PeriodicalIF":3.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035675","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}