Journal of Computational Physics最新文献

{"title":"Non-isothermal filtration problem: Two-temperature computational model","authors":"Maksim I. Ivanov,&nbsp;Igor A. Kremer,&nbsp;Yuri M. Laevsky","doi":"10.1016/j.jcp.2025.113941","DOIUrl":"10.1016/j.jcp.2025.113941","url":null,"abstract":"<div><div>The article proposes a new computational model of non-isothermal filtration of a two-phase incompressible fluid. From the point of view of applications, we are talking about the displacement of oil by water when hot water enters from an injection well. The specificity of the proposed model is its two-temperature formulation. The two-temperature formulation is understood as thermal heterogeneity, in which at each point of the domain under consideration the temperatures of the two-phase fluid and porous blocks are determined, and the thermal interaction between the two continua is indicated. The mathematical model is presented in a mixed formulation in the form of a system of first-order equations in terms of four scalar functions (liquid pressure, water saturation, liquid and porous medium temperatures) and three vector functions (total liquid velocity and heat conductive fluxes of the liquid and porous medium). The spatial approximation is based on a combination of mixed FEM and centered FVM. The time approximation consists of using an explicit-implicit scheme with upwinding. In particular, IMPES-type method is used for the filtration equations, and the energy equations explicitly consider convective transfer with the choice of time step according to the CFL condition. For heat exchange between the fluid and the porous medium, both explicit and implicit approximations are used. It is shown that the stability condition of the explicit scheme is significantly weaker than the CFL conditions for convective flows in the mass and energy conservation laws at an accuracy coinciding with the accuracy of the implicit scheme. Also, the two-temperature model made it possible to study the role of heat conductive transfer in a liquid.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113941"},"PeriodicalIF":3.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686534","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":"Constructing stable, high-order finite-difference operators on point clouds over complex geometries","authors":"Jason Hicken,&nbsp;Ge Yan ,&nbsp;Sharanjeet Kaur","doi":"10.1016/j.jcp.2025.113940","DOIUrl":"10.1016/j.jcp.2025.113940","url":null,"abstract":"<div><div>High-order difference operators with the summation-by-parts (SBP) property can be used to build stable discretizations of hyperbolic conservation laws; however, most high-order SBP operators require a conforming, high-order mesh for the domain of interest. To circumvent this requirement, we present an algorithm for building high-order, diagonal-norm, first-derivative SBP operators on point clouds over level-set geometries. The algorithm is <em>not</em> mesh-free, since it uses a Cartesian cut-cell mesh to define the sparsity pattern of the operators and to provide intermediate quadrature rules; however, the mesh is generated automatically and can be discarded once the SBP operators have been constructed. Using this temporary mesh, we construct local, cell-based SBP difference operators that are assembled into global SBP operators. We identify conditions for the existence of a positive-definite diagonal mass matrix, and we compute the diagonal norm by solving a sparse system of linear inequalities using an interior-point algorithm. We also describe an artificial dissipation operator that complements the first-derivative operators when solving hyperbolic problems, although the dissipation is not required for stability. The numerical results confirm the conditions under which a diagonal norm exists and study the distribution of the norm's entries. In addition, the results verify the accuracy and stability of the point-cloud SBP operators using the linear advection equation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113940"},"PeriodicalIF":3.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697991","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 level set immersed finite element method for parabolic problems on surfaces with moving interfaces","authors":"Jiaqi Chen ,&nbsp;Xufeng Xiao ,&nbsp;Xinlong Feng ,&nbsp;Dongwoo Sheen","doi":"10.1016/j.jcp.2025.113939","DOIUrl":"10.1016/j.jcp.2025.113939","url":null,"abstract":"<div><div>This paper addresses the challenge of solving parabolic moving interface problems on surfaces. These problems have diverse applications, including the Stefan problem, solidification of dendrites on solid surfaces, and flow patterns on soap bubbles. The main difficulties lie in accurately discretizing complex surfaces, efficiently processing interface jump conditions, and tracking the moving interface. Existing numerical methods for interface problems on surfaces have limitations, such as handling only homogeneous jump conditions, having first-order accuracy, or requiring body-fitted nodes. To overcome these limitations, this paper proposes a second-order accurate immersed finite element method (IFEM) for solving parabolic moving interface problems on surfaces. The method is extended to handle non-homogeneous flux jump conditions by enriching the basis functions on interface elements. Furthermore, a novel computational framework is proposed by combining the IFEM with the level set method to track the moving interface. This framework simulates the heat conduction process involving moving interfaces in different velocity fields. The innovation of this paper lies in its ability to handle moving interface problems on surfaces with improved accuracy, efficiency, and versatility compared to existing methods. Verified through numerical simulation, the proposed method and computational framework enable the simulation of a wider range of heat conduction with moving interfaces on surfaces.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113939"},"PeriodicalIF":3.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686401","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":"Energy and entropy conserving compatible finite elements with upwinding for the thermal shallow water equations","authors":"Tamara A. Tambyah ,&nbsp;David Lee ,&nbsp;Santiago Badia","doi":"10.1016/j.jcp.2025.113937","DOIUrl":"10.1016/j.jcp.2025.113937","url":null,"abstract":"<div><div>In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy–related quadratic tracer variances. Our approach relies on restating the governing equations to enable discontinuous approximations of thermodynamic variables and a variational continuous time integration. A key novelty is the inclusion of centred and upwinded fluxes. The proposed semi-discrete system conserves discrete entropy for centred fluxes, monotonically damps entropy for upwinded fluxes, and conserves energy. The fully discrete scheme preserves entropy conservation at the continuous level. The ability of a new linearised Jacobian, which accounts for both centred and upwinded fluxes, to capture large variations in buoyancy and simulate thermally unstable flows for long periods of time is demonstrated for two different transient case studies. The first involves a thermogeostrophic instability where including upwinded fluxes is shown to suppress spurious oscillations while successfully conserving energy and monotonically damping entropy. The second is a double vortex where a constrained fully discrete formulation is shown to achieve exact entropy conservation in time.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113937"},"PeriodicalIF":3.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal transport-based displacement interpolation with data augmentation for reduced order modeling of nonlinear dynamical systems","authors":"Moaad Khamlich ,&nbsp;Federico Pichi ,&nbsp;Michele Girfoglio ,&nbsp;Annalisa Quaini ,&nbsp;Gianluigi Rozza","doi":"10.1016/j.jcp.2025.113938","DOIUrl":"10.1016/j.jcp.2025.113938","url":null,"abstract":"<div><div>We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face challenges in this scenario, especially when data (i.e., observational snapshots) are limited, our method addresses these issues by introducing a data augmentation strategy based on OT principles. The proposed framework generates interpolated solutions tracing geodesic paths in the space of probability distributions, enriching the training dataset for the ROM. A key feature of our approach is its ability to provide a continuous representation of the solution's dynamics by exploiting a virtual-to-real time mapping. This enables the reconstruction of solutions at finer temporal scales than those provided by the original data. To further improve prediction accuracy, we employ Gaussian Process Regression to learn the residual and correct the representation between the interpolated snapshots and the physical solution.</div><div>We demonstrate the effectiveness of our methodology with atmospheric mesoscale benchmarks characterized by highly nonlinear, advection-dominated dynamics. Our results show improved accuracy and efficiency in predicting complex system behaviors, indicating the potential of this approach for a wide range of applications in computational physics and engineering.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113938"},"PeriodicalIF":3.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686533","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":"Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE","authors":"Jianbing Chen ,&nbsp;Tingting Sun ,&nbsp;Pol D. Spanos ,&nbsp;Jie Li","doi":"10.1016/j.jcp.2025.113929","DOIUrl":"10.1016/j.jcp.2025.113929","url":null,"abstract":"<div><div>Significant challenges persist for the reliable probabilistic analyses of high-dimensional nonlinear dynamical systems subject to multiplicative white noise, particularly at the level of probability density. To address this issue, an efficient method is proposed by employing the dimension-reduced probability density evolution equation (DR-PDEE) to determine the probability density of the responses in such systems. The starting point of the method is that, in many cases, only a limited number of quantities in a system are of interest. Thus, the corresponding DR-PDEE is a one- or two-dimensional partial differential equation (PDE) that governs the instantaneous probability density function (PDF) of the quantity/response(s) of interest in high-dimensional stochastic dynamical systems. This is with the stipulation that the response meets the path continuity condition, and there is no restriction on the excitations being multiplicative or additive. The intrinsic drift and diffusion functions in the DR-PDEE are conditional expectation functions of these responses of the original high-dimensional systems that can be reliably estimated, where assessing the latter is specific to multiplicative noise problems. Interestingly, for a wide class of systems subject to multiplicative local noise, the intrinsic diffusion functions are analytically determinable. Subsequently, the instantaneous PDF of the quantity of interest can be efficiently obtained by numerically integrating the one- or two-dimensional DR-PDEE. The accuracy and efficiency of the DR-PDEE are verified by several typical nonlinear high-dimensional dynamical systems. Particularly, the DR-PDEE captures accurately the refined traits that are easily overlooked, and the tail range of response PDFs.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113929"},"PeriodicalIF":3.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686398","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-oscillatory entropy stable DG schemes for hyperbolic conservation law","authors":"Yuchang Liu ,&nbsp;Wei Guo ,&nbsp;Yan Jiang ,&nbsp;Mengping Zhang","doi":"10.1016/j.jcp.2025.113926","DOIUrl":"10.1016/j.jcp.2025.113926","url":null,"abstract":"<div><div>In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly controls entropy production and suppresses spurious oscillations. To address the stiffness introduced by the artificial terms, which can restrict severely time step sizes, we employ the integrating factor strong stability-preserving Runge-Kutta method for time discretization. Furthermore, our method remains compatible with positivity-preserving limiters under suitable CFL conditions in extreme cases. Various numerical examples demonstrate the efficiency of the proposed scheme, showing that it maintains high-order accuracy in smooth regions and avoids spurious oscillations near discontinuities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113926"},"PeriodicalIF":3.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644167","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":"Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections","authors":"Dong Min Roh ,&nbsp;Dean Lee ,&nbsp;Pieter Maris ,&nbsp;Esmond Ng ,&nbsp;James P. Vary ,&nbsp;Chao Yang","doi":"10.1016/j.jcp.2025.113921","DOIUrl":"10.1016/j.jcp.2025.113921","url":null,"abstract":"<div><div>Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113921"},"PeriodicalIF":3.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644163","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 generalized transformed path integral approach for stochastic processes","authors":"Gnana Murugan Subramaniam,&nbsp;Prakash Vedula","doi":"10.1016/j.jcp.2025.113925","DOIUrl":"10.1016/j.jcp.2025.113925","url":null,"abstract":"<div><div>In this paper, we present the generalized transformed path integral (GTPI) approach: a grid-based path integral approach for probabilistic description in a large class of stochastic dynamical systems. We showcase the application of our proposed approach to non-singular systems, as well as to singular systems such as second-order (and higher-order) dynamical systems, dynamical systems with zero process noise, and certain dynamical systems with non-white noise excitation. As a part of the approach, we present a novel framework for the description of stochastic dynamical systems in terms of a complementary system—the standard transformed stochastic dynamical system—obtained through a dynamic transformation of the state variables. The state mean and covariance of the transformed system do not change with evolution and the choice of our transformation parameters ensure that they are zero and identity respectively. Thus, the probability density function (PDF) for the state of the transformed system can be evolved in a transformed space where greater numerical accuracy for the distribution can be ensured. A fixed grid in the transformed space coordinates corresponds to an adaptive grid in the original space coordinates; it allows the proposed approach to more efficiently address the challenge of large drift, diffusion, or concentration of PDF in the stochastic dynamical system. In addition, error bounds for distributions in the transformed space can be easily obtained using Chebyshev's inequality. We use an operator splitting–based solution of the Fokker-Planck equation associated with the transformed system to derive a novel short-time propagator and update relations for the evolution of the transformed state PDF in the transformed space. Necessary update relations for the mean and covariance of the original state variables, used in the evolution of the transformed state PDF, are derived from the underlying stochastic models. Illustrative examples were considered to showcase the benefits of the GTPI approach over conventional fixed grid (FG) approaches in a large class of stochastic dynamical systems. In all the cases, results obtained using the GTPI approach show excellent agreement with results from Monte Carlo simulations and available analytical (and stationary) solutions, while results from the FG approach show large errors. The effect of simulation parameters and system parameters on the numerical error in our approach were also studied.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113925"},"PeriodicalIF":3.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644165","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":"Mathematical theory and numerical method for subwavelength resonances in multi-layer high contrast elastic media","authors":"Yajuan Wang,&nbsp;Youjun Deng,&nbsp;Fanbo Sun,&nbsp;Lingzheng Kong","doi":"10.1016/j.jcp.2025.113924","DOIUrl":"10.1016/j.jcp.2025.113924","url":null,"abstract":"<div><div>In this paper, we develop a rigorous mathematical framework and numerical method for analyzing and computing the subwavelength resonances of multi-layer structures in elastic system, respectively. The system considered is constituted of a finite alternance of high-contrast segments, called the “resonators”, and a background medium. Firstly, based on layer potential theory, we derive an integral equation explicitly involving the geometric and material configurations. By the Gohberg-Sigal theory, it is theoretically demonstrated that the number of resonance frequencies increases as the number of resonators increases. There are <span><math><mn>6</mn><mo>⋅</mo><mo>⌈</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></math></span> resonance frequencies for <span><math><mo>⌈</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></math></span> resonators (high contrast domain) within the <em>N</em>-layer structure. In addition, we derive the quantitative expressions for the subwavelength resonance frequencies within concentric balls, i.e., coaxial resonators, calculated by solving the corresponding eigenvalue problem of an explicit matrix. Finally, some numerical experiments are also provided to collaborate with the theoretical results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113924"},"PeriodicalIF":3.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644164","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}