Journal of Computational Physics最新文献

{"title":"Implementation of integral surface tension formulations in a volume of fluid framework and their applications to Marangoni flows","authors":"Mandeep Saini ,&nbsp;Vatsal Sanjay ,&nbsp;Youssef Saade ,&nbsp;Detlef Lohse ,&nbsp;Stéphane Popinet","doi":"10.1016/j.jcp.2025.114348","DOIUrl":"10.1016/j.jcp.2025.114348","url":null,"abstract":"<div><div>Accurate numerical modeling of surface tension has been a challenging aspect of multiphase flow simulations. The integral formulation for modeling surface tension forces is known to be consistent and conservative, and to be a natural choice for the simulation of flows driven by surface tension gradients along the interface. This formulation was introduced by Popinet and Zaleski [1] for a front-tracking method and was later extended to level set methods by Al-Saud et al. [2]. In this work, we extend the integral formulation to a volume of fluid (VOF) method for capturing the interface. In fact, we propose three different schemes distinguished by the way we calculate the geometric properties of the interface, namely curvature, tangent vector and surface fraction from VOF representation. We propose a coupled level set volume of fluid (CLSVOF) method in which we use a signed distance function coupled with VOF, a height function (HF) method in which we use the height functions calculated from VOF, and a height function to distance (HF2D) method in which we use a sign-distance function calculated from height functions. For validation, these methods are rigorously tested for several problems with constant as well as varying surface tension. It is found that from an accuracy standpoint, CLSVOF has the least numerical oscillations followed by HF2D and then HF. However, from a computational speed point of view, HF method is the fastest followed by HF2D and then CLSVOF. Therefore, the HF2D method is a good compromise between speed and accuracy for obtaining faster and correct results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114348"},"PeriodicalIF":3.8,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057316","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 simple and general framework for the construction of exactly div-curl-grad compatible discontinuous Galerkin finite element schemes on unstructured simplex meshes","authors":"R. Abgrall ,&nbsp;M. Dumbser ,&nbsp;P.-H Maire","doi":"10.1016/j.jcp.2025.114340","DOIUrl":"10.1016/j.jcp.2025.114340","url":null,"abstract":"<div><div>We introduce a new family of discontinuous Galerkin (DG) finite element schemes for the discretization of first order systems of hyperbolic partial differential equations (PDE) on unstructured simplex meshes in two and three space dimensions that respect the two basic vector calculus identities exactly also at the discrete level, namely that the curl of the gradient is zero and that the divergence of the curl is zero. The key ingredient here is the construction of two compatible discrete nabla operators, a primary one and a dual one, both defined on general unstructured simplex meshes in multiple space dimensions. Our new schemes extend existing cell-centered finite volume methods based on corner fluxes to arbitrary high order of accuracy in space. An important feature of our new method is the fact that only two different discrete function spaces are needed to represent the numerical solution, and the choice of the appropriate function space for each variable is related to the origin and nature of the underlying PDE. The first class of variables is discretized at the aid of a <em>discontinuous</em> Galerkin approach, where the numerical solution is represented via piecewise polynomials of degree <span><math><mi>N</mi></math></span> and which are allowed to jump across element interfaces. This set of variables is related to those PDE which are mere consequences of the definitions, derived from some abstract scalar and vector potentials, and for which involutions like the divergence-free or the curl-free property must hold if satisfied by the initial data. The second class of variables is discretized via classical <em>continuous</em> Lagrange finite elements of approximation degree <span><math><mrow><mi>M</mi><mo>=</mo><mi>N</mi><mo>+</mo><mn>1</mn></mrow></math></span> and is related to those PDE which can be derived as the Euler-Lagrange equations of an underlying variational principle.</div><div>The primary nabla operator takes as input the data from the FEM space and returns data in the DG space, while the dual nabla operator takes as input the data from the DG space and produces output in the FEM space. The two discrete nabla operators satisfy a discrete Schwarz theorem on the symmetry of discrete second derivatives. From there, both discrete vector calculus identities follow automatically.</div><div>We apply our new family of schemes to three hyperbolic systems with involutions: the system of linear acoustics, in which the velocity field must remain curl-free and the vacuum Maxwell equations, in which the divergence of the magnetic field and of the electric field must remain zero. In our approach, only the magnetic field will remain exactly divergence free. As a third model we study the Maxwell-GLM system of Munz et al. [1], which contains a unique mixture of curl-curl and div-grad operators and in which the magnetic field may be either curl-free or divergence-free, depending on the choice of the initial data. In all cases we prove ","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114340"},"PeriodicalIF":3.8,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145045036","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":"Tensor decomposition-based DEIM for model order reduction applied to nonlinear parametric electromagnetic problems","authors":"Ze Guo ,&nbsp;Zuqi Tang ,&nbsp;Zhuoxiang Ren","doi":"10.1016/j.jcp.2025.114352","DOIUrl":"10.1016/j.jcp.2025.114352","url":null,"abstract":"<div><div>Projection-based model order reduction (MOR) is a key technique in digital twins, enabling the rapid generation of large-scale, high-fidelity, parametric simulation data through numerical methods. However, a major challenge in projection-based MOR is the evaluation of nonlinear terms, which depend on the size of the full-order model during the iterative process. This reliance significantly degrades the efficiency of MOR techniques. While various hyper-reduction technique, such as the discrete empirical interpolation method (DEIM) discussed in this paper, have been introduced to mitigate this issue by employing low-dimensional representation to approximate nonlinear terms and accelerate computations, classical DEIM faces notable limitations in practical applications. Specifically, when a system’s nonlinear characteristics vary significantly with parameters, it becomes difficult to create a universal low-dimensional representation capable of capturing nonlinear behavior across the entire parameter space. Additionally, as the number of system parameters increases, the low-dimensional representation grows in size, reducing its computational efficiency for nonlinear term evaluations.</div><div>To address these challenges, we build upon the two-stage model reduction approach that leverages tensor structures, originally proposed by Mamonov and Olshanskii for linear systems (Comput. Methods Appl. Mech. Engrg., 397, 115122, 2022) and later further developed for nonlinear dynamical systems with DEIM in (SIAM J. Sci. Comput., 46(3), A1850–A1878, 2024). Inspired by these contributions, we adapt and extend the methodology to address time-independent parametric problems, with a particular focus on electromagnetic applications. This approach dynamically generates problem-dependent and parameter-specific low-dimensional representation for the nonlinear terms. Its performance is demonstrated through various numerical examples, including an EI transformer with varying excitation, an electric motor under operational variations, and a voice coil actuator (VCA) with non-uniform demagnetization. Results show that this approach significantly outperforms classical DEIM in terms of efficiency and accuracy.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114352"},"PeriodicalIF":3.8,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048013","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 Eulerian variance-based finite-time Lyapunov exponent (vFTLE) approach for flows with uncertainties","authors":"Guoqiao You ,&nbsp;Wai Ming Chau ,&nbsp;Shingyu Leung","doi":"10.1016/j.jcp.2025.114353","DOIUrl":"10.1016/j.jcp.2025.114353","url":null,"abstract":"<div><div>We propose a novel partial differential equation (PDE) approach for computing the variance-based finite-time Lyapunov exponent (vFTLE) in stochastic vector fields. Our method modifies and extends finite-time variance analysis (FTVA) by incorporating the covariance matrix of the probability density function (PDF) associated with each initial takeoff location. This approach allows us to utilize the maximum eigenvalue of the covariance matrix to approximate the maximal stretching rate in uncertain flows. Additionally, we enhance computational efficiency by integrating stochastic sensitivity into an Eulerian framework, enabling the identification of regions with significant vFTLE values. This combination improves both the accuracy and efficiency of analyzing complex flow dynamics in stochastic environments.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114353"},"PeriodicalIF":3.8,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019862","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 with coordinate transformation to solve high Reynolds number boundary layer flows","authors":"Zhen Zhang,&nbsp;Xinrong Su,&nbsp;Xin Yuan","doi":"10.1016/j.jcp.2025.114338","DOIUrl":"10.1016/j.jcp.2025.114338","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) are a promising way to solve partial differential equations in forward or inverse mode. Compared with traditional numerical methods, PINNs have distinct advantages in solving inverse as well as parametric problems. However, for complicated flows such as high Reynolds number boundary layer, where large velocity gradients appear near the wall, PINNs are difficult to converge and sometimes give meaningless solutions. To deal with this issue, we introduce the coordinate transformation technique to scale up the boundary layer region and solve PINNs in a computational space where the large gradients are significantly reduced. A flat plate boundary layer and the NACA0012 airfoil are calculated, and the Reynolds number of both cases is in the order of millions. Results show that PINNs with coordinate transformation can satisfactorily solve high Reynolds boundary layer flows that are nearly impossible for vanilla PINNs.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114338"},"PeriodicalIF":3.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019861","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":"Numerical simulations of the phase behaviors of rod-coil diblock copolymers confined on a spherical surface","authors":"Jiahui Luo ,&nbsp;Qin Liang ,&nbsp;Yunqing Huang","doi":"10.1016/j.jcp.2025.114339","DOIUrl":"10.1016/j.jcp.2025.114339","url":null,"abstract":"<div><div>The self-assembly of rod-coil diblock copolymers has garnered significant attention owing to their intricate phase behavior. One of the most successful theories to investigate these phase behaviors is the self-consistent field theory (SCFT). In this work, we employ SCFT to study the phase behavior of rod-coils when these polymers are confined on a spherical surface. While such confinement enriches the diversity of possible phases, it also increases the complexity of the numerical simulations with SCFT. To address this challenge, we develop a novel pseudo-spectral method that employs spherical harmonics, the Wigner D-matrix, and a time-splitting approach to efficiently solve the Fokker-Planck equations in SCFT. The interplay between the liquid crystalline nature of the rod-like units, microphase separation, and spherical confinement results in a remarkable diversity of morphologies. The choice of initial fields plays a crucial role in determining the final converged states. To facilitate the generation of initial states for various striped structures, we propose a cut-and-rotate method. Using this numerical framework, we systematically investigate the phase behavior of rod-coil diblock copolymers over a range of sphere radii. For rod-coils with symmetric composition, we observe a sequence of stable striped patterns, including lamellar, single-helical, and double-helical structures, which alternate as the sphere radius increases. For asymmetric compositions, spotted patterns emerge as stable configurations. These findings provide new insights into the self-assembly of rod-coil copolymers under spherical confinement and underscore the utility of advanced numerical techniques for exploring complex phase behaviors.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114339"},"PeriodicalIF":3.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145045130","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":"Structure-preserving and thermodynamically consistent finite element discretization for visco-resistive MHD with thermoelectric effect","authors":"Evan S. Gawlik ,&nbsp;François Gay-Balmaz ,&nbsp;Bastien Manach-Pérennou","doi":"10.1016/j.jcp.2025.114336","DOIUrl":"10.1016/j.jcp.2025.114336","url":null,"abstract":"<div><div>We present a structure-preserving and thermodynamically consistent numerical scheme for classical magnetohydrodynamics, incorporating viscosity, magnetic resistivity, heat transfer, and thermoelectric effect. The governing equations are shown to be derived from a generalized Hamilton’s principle, with the resulting weak formulation being mimicked at the discrete level. The resulting numerical method conserves mass and energy, satisfies Gauss’ magnetic law and magnetic helicity balance, and adheres to the Second Law of Thermodynamics, all at the fully discrete level. It is shown to perform well on magnetic Rayleigh–Bénard convection.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114336"},"PeriodicalIF":3.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048012","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":"Software-based automatic differentiation is flawed","authors":"Daniel Johnson ,&nbsp;Trevor Maxfield ,&nbsp;Yongxu Jin ,&nbsp;Ronald Fedkiw","doi":"10.1016/j.jcp.2025.114319","DOIUrl":"10.1016/j.jcp.2025.114319","url":null,"abstract":"<div><div>Software efforts in automatic differentiation are built on the observation that every computation is implemented as a series of elementary operations, and that symbolic partial derivatives can be supplied for each of these operations. Any computation can then be traversed (either forwards or backwards) utilizing the chain rule to accumulate derivatives. These frameworks have no mechanism for simplifying these expressions before evaluating them. As we illustrate below, the resulting errors tend to be unbounded.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114319"},"PeriodicalIF":3.8,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097620","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 dynamic domain semi-Lagrangian method for stochastic Vlasov equations","authors":"Jianbo Cui ,&nbsp;Derui Sheng ,&nbsp;Chenhui Zhang ,&nbsp;Tau Zhou","doi":"10.1016/j.jcp.2025.114335","DOIUrl":"10.1016/j.jcp.2025.114335","url":null,"abstract":"<div><div>We propose a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noise, which arise in plasma physics and astrophysics. This method combines the volume-preserving property of stochastic characteristics with a dynamic domain adaptation strategy and a reconstruction procedure. It offers a substantial reduction in computational costs compared to the traditional semi-Lagrangian techniques for stochastic problems. Furthermore, we present the first-order convergence analysis of the proposed method, partially addressing the conjecture in [1] on the convergence order of numerical methods for stochastic Vlasov equations. Several numerical tests are provided to show good performance of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114335"},"PeriodicalIF":3.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026556","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":"Very high-order multi-layer compact schemes with shock-fitting method (MLC-SF) for compressible flow simulations","authors":"Yung-Tien Lin,&nbsp;Xiaolin Zhong","doi":"10.1016/j.jcp.2025.114332","DOIUrl":"10.1016/j.jcp.2025.114332","url":null,"abstract":"&lt;div&gt;&lt;div&gt;High-order numerical methods are commonly employed in direct numerical simulation (DNS) to achieve the required accuracy with fewer degrees of freedom, thereby improving computational efficiency. To further improve global spatial accuracy, Bai and Zhong proposed the multi-layer compact (MLC) schemes (JCP, 2019) to introduce spatial derivatives as new degrees of freedom and create a more compact stencil for the same spatial accuracy. Stability analysis showed MLC can achieve seventh-order global accuracy with closed boundaries, which surpasses most of the sixth-order conventional upwind finite difference schemes. Despite this high-order convergence rate, MLC faces challenges in supersonic flow simulations, primarily due to the Gibbs phenomenon across shock waves. The numerical oscillation can cause divergence in high-order numerical schemes if no additional treatment, such as shock-capturing or shock-fitting methods, is applied. Therefore, further studies are needed to enhance MLC’s applicability to realistic high-speed flow applications, particularly in the context of shock treatments and boundary condition implementation. This paper develops a novel MLC method to improve its applicability for supersonic flow simulations. The proposed method integrates MLC with the shock-fitting method (MLC-SF), treating the shock wave as a computational boundary that separates upstream and downstream solutions. The shock-fitting method mitigates spurious numerical oscillations across the discontinuous interface, preserving the high-order accuracy of MLC-SF. Additionally, this paper introduces a physically consistent boundary condition for the MLC-SF spatial derivative layers behind the shock. This boundary condition uses the inversion of the flux Jacobian matrix to estimate the correct spatial derivatives, ensuring consistency between MLC-SF value and derivative layers at the inflow boundary. In order to systematically benchmark the proposed method, MLC-SF is applied to five simulation cases involving linear advection, Euler, and Navier-Stokes equations on one- and two-dimensional domains. The studied cases aim to compare the results of shock-fitting and shock-capturing methods, evaluate the performance of MLC-SF within the arbitrary Lagrangian-Eulerian (ALE) framework for moving grid applications, and test the MLC-SF derivative layers on fluid mechanics problems involving non-Cartesian grids. In both one-dimensional and two-dimensional shock wave interaction cases, MLC-SF with the proposed physically consistent inflow condition achieves seventh-order spatial accuracy, which outperforms the other four tested methods. Notably, in the one-dimensional shock-interaction results, the fifth-order WENO methods exhibit only first-order accuracy behind the shock wave, highlighting the necessity of adopting the shock-fitting approach to maintain the high spatial accuracy property in MLC-SF. In terms of computational efficiency. MLC-SF can save at least 30 % of t","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114332"},"PeriodicalIF":3.8,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010101","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}