Pub Date : 2025-12-25DOI: 10.1016/j.jcp.2025.114615
Antoine Quiriny , Václav Kučera , Jonathan Lambrechts , Nicolas Moës , Jean-François Remacle
In this paper, we propose a new approach – the Tempered Finite Element Method (TFEM) – that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM approaches do not allow convergence. First, we review why the maximum angle condition [1] is not necessary for FEM convergence and what are the real limitations in terms of meshes. Next, we propose a simple modification of the classical FEM for elliptic problems that provably allows convergence for a wider class of meshes including bands of caps that cause locking of the solution in standard FEM formulations. The proposed method is trivial to implement in an existing FEM code and can be theoretically analyzed. We prove that in the case of exactly zero-measure elements it corresponds to mortaring. We show numerically and theoretically that what we propose is functional and sound. The remainder of the paper is devoted to extensions of the TFEM method to linear elasticity, mortaring of non-conforming meshes, high-order elements, and advection.
{"title":"The tempered finite element method","authors":"Antoine Quiriny , Václav Kučera , Jonathan Lambrechts , Nicolas Moës , Jean-François Remacle","doi":"10.1016/j.jcp.2025.114615","DOIUrl":"10.1016/j.jcp.2025.114615","url":null,"abstract":"<div><div>In this paper, we propose a new approach – the Tempered Finite Element Method (TFEM) – that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM approaches do not allow convergence. First, we review why the maximum angle condition [1] is not necessary for FEM convergence and what are the real limitations in terms of meshes. Next, we propose a simple modification of the classical FEM for elliptic problems that provably allows convergence for a wider class of meshes including bands of caps that cause locking of the solution in standard FEM formulations. The proposed method is trivial to implement in an existing FEM code and can be theoretically analyzed. We prove that in the case of exactly zero-measure elements it corresponds to mortaring. We show numerically and theoretically that what we propose is functional and sound. The remainder of the paper is devoted to extensions of the TFEM method to linear elasticity, mortaring of non-conforming meshes, high-order elements, and advection.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114615"},"PeriodicalIF":3.8,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882119","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}
Pub Date : 2025-12-24DOI: 10.1016/j.jcp.2025.114619
Swapnil Mache , Ivo M. Vellekoop
The modified Born series (MBS) is a fast and accurate method for simulating wave propagation in complex structures. In the current implementation of the MBS, the simulation size is limited by the working memory of a single computer or graphics processing unit (GPU). Here, we present a domain decomposition method that enhances the scalability of the MBS by distributing the computations over multiple GPUs, while maintaining its accuracy, memory efficiency, and guaranteed monotonic convergence. With this new method, the computations can be performed in parallel, and a larger simulation size is possible as it is no longer limited to the memory size of a single computer or GPU. We show how to decompose large problems over subdomains and demonstrate our approach by solving the Helmholtz problem for a complex structure of 3.28 · 107 cubic wavelengths (320 × 320 × 320 wavelengths) in just 45 minutes with a dual-GPU simulation.
{"title":"Domain decomposition of the modified Born series approach for large-scale wave propagation simulations","authors":"Swapnil Mache , Ivo M. Vellekoop","doi":"10.1016/j.jcp.2025.114619","DOIUrl":"10.1016/j.jcp.2025.114619","url":null,"abstract":"<div><div>The modified Born series (MBS) is a fast and accurate method for simulating wave propagation in complex structures. In the current implementation of the MBS, the simulation size is limited by the working memory of a single computer or graphics processing unit (GPU). Here, we present a domain decomposition method that enhances the scalability of the MBS by distributing the computations over multiple GPUs, while maintaining its accuracy, memory efficiency, and guaranteed monotonic convergence. With this new method, the computations can be performed in parallel, and a larger simulation size is possible as it is no longer limited to the memory size of a single computer or GPU. We show how to decompose large problems over subdomains and demonstrate our approach by solving the Helmholtz problem for a complex structure of 3.28 · 10<sup>7</sup> cubic wavelengths (320 × 320 × 320 wavelengths) in just 45 minutes with a dual-GPU simulation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114619"},"PeriodicalIF":3.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974702","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}
The M1 moment model for electron transport is commonly used to describe non-local thermal transport effects in laser-plasma simulations. In this article, we propose a new asymptotic-preserving scheme based on the Unified Gas Kinetic Scheme (UGKS) for this model in two-dimensional space. This finite volume kinetic scheme follows the same approach as in our previous article [1] and relies on a moment closure, at the numerical scale, of the microscopic flux of UGKS. The method is developed for both structured and unstructured meshes, and several techniques are introduced to ensure accurate fluxes in the diffusion limit. A second-order extension is also proposed. Several test cases validate the different aspects of the scheme and demonstrate its efficiency in multiscale simulations. In particular, the results demonstrate that this method accurately captures non-local thermal effects.
{"title":"An asymptotic preserving kinetic scheme for the M1 model of non-local thermal transport for two-dimensional structured and unstructured meshes","authors":"Jean-Luc Feugeas , Julien Mathiaud , Luc Mieussens , Thomas Vigier","doi":"10.1016/j.jcp.2025.114618","DOIUrl":"10.1016/j.jcp.2025.114618","url":null,"abstract":"<div><div>The M1 moment model for electron transport is commonly used to describe non-local thermal transport effects in laser-plasma simulations. In this article, we propose a new asymptotic-preserving scheme based on the Unified Gas Kinetic Scheme (UGKS) for this model in two-dimensional space. This finite volume kinetic scheme follows the same approach as in our previous article [1] and relies on a moment closure, at the numerical scale, of the microscopic flux of UGKS. The method is developed for both structured and unstructured meshes, and several techniques are introduced to ensure accurate fluxes in the diffusion limit. A second-order extension is also proposed. Several test cases validate the different aspects of the scheme and demonstrate its efficiency in multiscale simulations. In particular, the results demonstrate that this method accurately captures non-local thermal effects.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114618"},"PeriodicalIF":3.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974705","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}
In this paper, we propose a linear, unconditionally energy-stable, and fully discrete finite element method for an incompressible ferrohydrodynamics flow. Consider the constitutive equations that model the motion of a magnetic fluid, proposed by Rosensweig. The Rosensweig model comprises the Navier-Stokes equations, the angular momentum equations, the magnetization equation, and the magnetostatics equation. An equivalent form of the magnetostatics equation is derived, which helps us to design an unconditionally stable discrete scheme. We propose a new fully discrete finite element method with second-order temporal accuracy, which preserves the original energy. We linearize the discrete problem with extrapolated solutions. The unconditional stability of the fully discrete solution is proved. Furthermore, we obtain the existence and uniqueness of the fully discrete solution by the Leray-Schauder fixed point theorem. Numerical experiments verify the effectiveness and accuracy of the scheme, and simulate the controllability of the magnetic fluid driven by an applied magnetic field.
{"title":"A fully discrete finite element method with second-order temporal accuracy for the Rosensweig model","authors":"Xiaojing Dong , Huayi Huang , Yunqing Huang , Xiaofeng Yang","doi":"10.1016/j.jcp.2025.114617","DOIUrl":"10.1016/j.jcp.2025.114617","url":null,"abstract":"<div><div>In this paper, we propose a linear, unconditionally energy-stable, and fully discrete finite element method for an incompressible ferrohydrodynamics flow. Consider the constitutive equations that model the motion of a magnetic fluid, proposed by Rosensweig. The Rosensweig model comprises the Navier-Stokes equations, the angular momentum equations, the magnetization equation, and the magnetostatics equation. An equivalent form of the magnetostatics equation is derived, which helps us to design an unconditionally stable discrete scheme. We propose a new fully discrete finite element method with second-order temporal accuracy, which preserves the original energy. We linearize the discrete problem with extrapolated solutions. The unconditional stability of the fully discrete solution is proved. Furthermore, we obtain the existence and uniqueness of the fully discrete solution by the Leray-Schauder fixed point theorem. Numerical experiments verify the effectiveness and accuracy of the scheme, and simulate the controllability of the magnetic fluid driven by an applied magnetic field.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114617"},"PeriodicalIF":3.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882033","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}
Pub Date : 2025-12-24DOI: 10.1016/j.jcp.2025.114631
Yanyu Chen (陈彦宇), Longzhang Huang (黄泷章), Wenjiang Xu (徐文江), Fan Yang (杨帆)
High-resolution three-dimensional swirling flame imaging is a vital diagnostic tool for combustion analysis, providing essential data for downstream tasks such as component concentration measurement and chemical reaction rate estimation in diverse combustion scenarios. Currently, in the field of super-resolution for actual physical scenes like combustion fields, diffusion models have achieved notable success due to their powerful data modeling capabilities and show considerable potential for widespread application. However, issues such as numerous timesteps, long inference times, and high computational resource consumption are more pronounced when these models are applied to complex three-dimensional flow field data. The 3D-SPCDM proposed in this paper optimizes the diffusion model by constructing a Markov chain between low- and high-resolution three-dimensional flame data, leading to the development of a more suitable loss function for the model. Additionally, we refine the weight allocation of skip-connections in the U-Net network architecture. These modifications significantly reduce the number of timesteps and the computational overhead during training and inference, while also avoiding the noise introduced by overly long Markov chains in the original diffusion model paradigm. Consequently, this enhances convergence speed and the accuracy of distribution estimation. The architectural improvements also boost the model's ability to reconstruct flame data details and express non-linear features, ensuring that the final reconstruction is physically more realistic and reliable. Experimental results from the super-resolution comparison of three-dimensional swirling flames demonstrate that our method achieves a PSNR improvement of 10.4% and 18.6% compared to 3D-PCDM in 8× and 64× voxel super-resolution experiments, respectively. It also performs excellently in SSIM and MAE evaluation metrics, providing clearer and more accurate representations of flame details. Furthermore, the method reduces the model parameter count by approximately 51.4%, effectively lowering computational resource consumption.
{"title":"Efficient High-Fidelity Three-dimensional Super-Resolution Reconstruction of Swirling Flame via Spaced Physically Consistent Diffusion Model","authors":"Yanyu Chen (陈彦宇), Longzhang Huang (黄泷章), Wenjiang Xu (徐文江), Fan Yang (杨帆)","doi":"10.1016/j.jcp.2025.114631","DOIUrl":"10.1016/j.jcp.2025.114631","url":null,"abstract":"<div><div>High-resolution three-dimensional swirling flame imaging is a vital diagnostic tool for combustion analysis, providing essential data for downstream tasks such as component concentration measurement and chemical reaction rate estimation in diverse combustion scenarios. Currently, in the field of super-resolution for actual physical scenes like combustion fields, diffusion models have achieved notable success due to their powerful data modeling capabilities and show considerable potential for widespread application. However, issues such as numerous timesteps, long inference times, and high computational resource consumption are more pronounced when these models are applied to complex three-dimensional flow field data. The 3D-SPCDM proposed in this paper optimizes the diffusion model by constructing a Markov chain between low- and high-resolution three-dimensional flame data, leading to the development of a more suitable loss function for the model. Additionally, we refine the weight allocation of skip-connections in the U-Net network architecture. These modifications significantly reduce the number of timesteps and the computational overhead during training and inference, while also avoiding the noise introduced by overly long Markov chains in the original diffusion model paradigm. Consequently, this enhances convergence speed and the accuracy of distribution estimation. The architectural improvements also boost the model's ability to reconstruct flame data details and express non-linear features, ensuring that the final reconstruction is physically more realistic and reliable. Experimental results from the super-resolution comparison of three-dimensional swirling flames demonstrate that our method achieves a PSNR improvement of 10.4% and 18.6% compared to 3D-PCDM in 8× and 64× voxel super-resolution experiments, respectively. It also performs excellently in SSIM and MAE evaluation metrics, providing clearer and more accurate representations of flame details. Furthermore, the method reduces the model parameter count by approximately 51.4%, effectively lowering computational resource consumption.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114631"},"PeriodicalIF":3.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882036","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}
Pub Date : 2025-12-24DOI: 10.1016/j.jcp.2025.114607
Lei Wu
The linear stability analysis of rarefied gas flows based on the Boltzmann kinetic equation has recently garnered research interest due to its potential applications in the high-altitude hypersonic flows, where rarefaction effects can render the Navier-Stokes equations invalid. Since the Boltzmann equation is defined in a six-dimensional phase space, directly solving the associated eigenvalue problems is computationally intractable. In this paper, we propose an efficient iterative method to solve the linear stability equation. The solution process involves both outer and inner iterations. In the outer iteration, the shifted inverse power method is employed to compute selected eigenvalues and their corresponding eigenfunctions of interest. For the inner iteration, which involves inverting the high-dimensional system for the velocity distribution function, we adopt our recently developed general synthetic iterative scheme to ensure fast-converging and asymptotic-preserving properties. As a proof of concept, our method demonstrates both high efficiency and accuracy in planar sound wave and Couette flow. Each eigenpair can be computed with only a few hundred iterations of the kinetic equation, and the spatial cell size can be significantly larger than the molecular mean free path in near-continuum flow regimes. In particular, for the sound problem, we observe for the first time that when the mean free path of gas molecules is comparable to the sound wavelength, large discrepancies arise among the results obtained from the Navier-Stokes equations, the Boltzmann equation with different viscosity indices (reflecting various intermolecular potentials such as hard-sphere, Maxwell, and shielded Coulomb interactions), and the simplified Shakhov kinetic model equation.
{"title":"Efficient solutions of eigenvalue problems in rarefied gas flows","authors":"Lei Wu","doi":"10.1016/j.jcp.2025.114607","DOIUrl":"10.1016/j.jcp.2025.114607","url":null,"abstract":"<div><div>The linear stability analysis of rarefied gas flows based on the Boltzmann kinetic equation has recently garnered research interest due to its potential applications in the high-altitude hypersonic flows, where rarefaction effects can render the Navier-Stokes equations invalid. Since the Boltzmann equation is defined in a six-dimensional phase space, directly solving the associated eigenvalue problems is computationally intractable. In this paper, we propose an efficient iterative method to solve the linear stability equation. The solution process involves both outer and inner iterations. In the outer iteration, the shifted inverse power method is employed to compute selected eigenvalues and their corresponding eigenfunctions of interest. For the inner iteration, which involves inverting the high-dimensional system for the velocity distribution function, we adopt our recently developed general synthetic iterative scheme to ensure fast-converging and asymptotic-preserving properties. As a proof of concept, our method demonstrates both high efficiency and accuracy in planar sound wave and Couette flow. Each eigenpair can be computed with only a few hundred iterations of the kinetic equation, and the spatial cell size can be significantly larger than the molecular mean free path in near-continuum flow regimes. In particular, for the sound problem, we observe for the first time that when the mean free path of gas molecules is comparable to the sound wavelength, large discrepancies arise among the results obtained from the Navier-Stokes equations, the Boltzmann equation with different viscosity indices (reflecting various intermolecular potentials such as hard-sphere, Maxwell, and shielded Coulomb interactions), and the simplified Shakhov kinetic model equation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114607"},"PeriodicalIF":3.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882060","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}
Pub Date : 2025-12-24DOI: 10.1016/j.jcp.2025.114612
Fengxiang Zhao , Kun Xu
This paper presents a generalized ENO (GENO)-type nonlinear reconstruction scheme for compressible flow simulations. The proposed reconstruction preserves the accuracy of the linear scheme while maintaining essentially non-oscillatory behavior at discontinuities. By generalizing the adaptive philosophy of ENO schemes, the method employs a smooth path function that directly connects high-order linear reconstruction with a reliable lower-order alternative. This direct adaptive approach significantly simplifies the construction of nonlinear schemes, particularly for very high-order methods on unstructured meshes. A comparative analysis with various WENO methods demonstrates the reliability and accuracy of the proposed reconstruction, which provides an optimal transition between linear and nonlinear reconstructions across all limiting cases based on stencil smoothness. The consistency and performance of the GENO reconstruction are validated through implementation in both high-order compact gas-kinetic schemes (GKS) and non-compact Riemann-solver-based schemes. Benchmark tests confirm the robustness and shock-capturing capabilities of GENO, with particularly superior performance when integrated with compact schemes. This work advances the construction methodology of nonlinear schemes and establishes ENO-type reconstruction as a mature and practical approach for engineering applications.
{"title":"A generalized ENO reconstruction in compact GKS for compressible flow simulations","authors":"Fengxiang Zhao , Kun Xu","doi":"10.1016/j.jcp.2025.114612","DOIUrl":"10.1016/j.jcp.2025.114612","url":null,"abstract":"<div><div>This paper presents a generalized ENO (GENO)-type nonlinear reconstruction scheme for compressible flow simulations. The proposed reconstruction preserves the accuracy of the linear scheme while maintaining essentially non-oscillatory behavior at discontinuities. By generalizing the adaptive philosophy of ENO schemes, the method employs a smooth path function that directly connects high-order linear reconstruction with a reliable lower-order alternative. This direct adaptive approach significantly simplifies the construction of nonlinear schemes, particularly for very high-order methods on unstructured meshes. A comparative analysis with various WENO methods demonstrates the reliability and accuracy of the proposed reconstruction, which provides an optimal transition between linear and nonlinear reconstructions across all limiting cases based on stencil smoothness. The consistency and performance of the GENO reconstruction are validated through implementation in both high-order compact gas-kinetic schemes (GKS) and non-compact Riemann-solver-based schemes. Benchmark tests confirm the robustness and shock-capturing capabilities of GENO, with particularly superior performance when integrated with compact schemes. This work advances the construction methodology of nonlinear schemes and establishes ENO-type reconstruction as a mature and practical approach for engineering applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114612"},"PeriodicalIF":3.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882061","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}
Pub Date : 2025-12-24DOI: 10.1016/j.jcp.2025.114609
Cecilia Pagliantini , Federico Vismara
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional model order reduction and hyper-reduction techniques are often ineffective for such models due to the non-sparse nature of the nonlinear operators arising from the interactions between particles. To tackle this issue, we propose an adaptive, structure-preserving hyper-reduction method that leverages a decomposition of the discrete reduced Hamiltonian into a linear combination of terms, each depending on a few components of the state. The proposed approximation strategy allows to: (i) preserve the Hamiltonian structure of the problem; (ii) evaluate nonlinear non-sparse operators in a computationally efficient way; (iii) overcome the Kolmogorov barrier of transport-dominated problems via evolution of the approximation space and adaptivity of the rank of the solution. The proposed method is validated on numerical benchmark simulations, demonstrating stable and accurate performance with substantial runtime reductions compared to the full order model.
{"title":"Adaptive hyper-reduction of non-sparse operators: Application to parametric particle-based kinetic plasma models","authors":"Cecilia Pagliantini , Federico Vismara","doi":"10.1016/j.jcp.2025.114609","DOIUrl":"10.1016/j.jcp.2025.114609","url":null,"abstract":"<div><div>This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional model order reduction and hyper-reduction techniques are often ineffective for such models due to the non-sparse nature of the nonlinear operators arising from the interactions between particles. To tackle this issue, we propose an adaptive, structure-preserving hyper-reduction method that leverages a decomposition of the discrete reduced Hamiltonian into a linear combination of terms, each depending on a few components of the state. The proposed approximation strategy allows to: (i) preserve the Hamiltonian structure of the problem; (ii) evaluate nonlinear non-sparse operators in a computationally efficient way; (iii) overcome the Kolmogorov barrier of transport-dominated problems via evolution of the approximation space and adaptivity of the rank of the solution. The proposed method is validated on numerical benchmark simulations, demonstrating stable and accurate performance with substantial runtime reductions compared to the full order model.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114609"},"PeriodicalIF":3.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922056","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}
Pub Date : 2025-12-23DOI: 10.1016/j.jcp.2025.114629
Changming Zhong , Zhaoli Guo , Xiafeng Zhou
A compact discrete unified gas kinetic scheme (CDUGKS) and its compact steady-state DUGKS (CSDUGKS) are developed in this work to solve a variety of particle-based multiscale transport problems. The core innovation lies in a compact reconstruction scheme, which determines the distribution function at cell interfaces using only local information within a single cell, thereby avoiding the use of data from multiple neighboring cells as in traditional DUGKS formulations. This compact reconstruction significantly enhances the accuracy and robustness of both original unsteady and steady DUGKS methods, particularly for strongly inhomogeneous problems on coarse meshes. The proposed compact reconstruction scheme is highly general and can be readily extended to various numerical limiters by incorporating compact gradients. It is also applicable to other frameworks, such as discrete velocity or ordinate methods and related transport solvers. Several representative particle-based multiscale transport problems—including phonon heat conduction, photon gray radiative transfer, and multigroup neutron transport—are conducted to assess the performance of the proposed CDUGKS and CSDUGKS. Numerical results demonstrate that the compact schemes outperform the original DUGKS and SDUGKS in terms of accuracy, particularly in configurations involving steep gradients, large optical thickness variations, and material discontinuities. Moreover, the compact reconstruction operates entirely within a single cell, making it particularly advantageous for massively parallel implementations. Overall, the proposed CDUGKS and CSDUGKS offer a robust, accurate, and scalable framework for solving complicated multiscale transport problems, and provide a promising basis for future extensions to large-scale practical engineering applications.
{"title":"Compact discrete unified gas kinetic scheme for unsteady and steady particle-based multiscale Boltzmann transport","authors":"Changming Zhong , Zhaoli Guo , Xiafeng Zhou","doi":"10.1016/j.jcp.2025.114629","DOIUrl":"10.1016/j.jcp.2025.114629","url":null,"abstract":"<div><div>A compact discrete unified gas kinetic scheme (CDUGKS) and its compact steady-state DUGKS (CSDUGKS) are developed in this work to solve a variety of particle-based multiscale transport problems. The core innovation lies in a compact reconstruction scheme, which determines the distribution function at cell interfaces using only local information within a single cell, thereby avoiding the use of data from multiple neighboring cells as in traditional DUGKS formulations. This compact reconstruction significantly enhances the accuracy and robustness of both original unsteady and steady DUGKS methods, particularly for strongly inhomogeneous problems on coarse meshes. The proposed compact reconstruction scheme is highly general and can be readily extended to various numerical limiters by incorporating compact gradients. It is also applicable to other frameworks, such as discrete velocity or ordinate methods and related transport solvers. Several representative particle-based multiscale transport problems—including phonon heat conduction, photon gray radiative transfer, and multigroup neutron transport—are conducted to assess the performance of the proposed CDUGKS and CSDUGKS. Numerical results demonstrate that the compact schemes outperform the original DUGKS and SDUGKS in terms of accuracy, particularly in configurations involving steep gradients, large optical thickness variations, and material discontinuities. Moreover, the compact reconstruction operates entirely within a single cell, making it particularly advantageous for massively parallel implementations. Overall, the proposed CDUGKS and CSDUGKS offer a robust, accurate, and scalable framework for solving complicated multiscale transport problems, and provide a promising basis for future extensions to large-scale practical engineering applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114629"},"PeriodicalIF":3.8,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882117","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}
Pub Date : 2025-12-23DOI: 10.1016/j.jcp.2025.114590
Junkai Wang, Qiaolin He
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable, characterized by the proposed temperature governing equation, rather than being derived from intermediate variables such as total energy density, internal energy density or entropy density. The hydrodynamic boundary conditions, which represent a generalization of the generalized Navier slip boundary condition for non-isothermal flows, are imposed in the proposed model. We then derive the dimensionless form of the model and prove that it rigorously satisfies both the first and second laws of thermodynamics. Based on the dimensionless system, an efficient numerical scheme is constructed by extending the multiple scalar auxiliary variable approach to the entropy production. The resulting scheme is decoupled, linear, unconditionally entropy-stable, and preserves mass conservation as well as the boundedness of number density at the fully discrete level. Several numerical results are presented to validate the effectiveness and stability of the proposed method.
{"title":"Thermodynamically consistent modeling and simulation of the moving contact line problem in non-isothermal two-phase flows","authors":"Junkai Wang, Qiaolin He","doi":"10.1016/j.jcp.2025.114590","DOIUrl":"10.1016/j.jcp.2025.114590","url":null,"abstract":"<div><div>According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable, characterized by the proposed temperature governing equation, rather than being derived from intermediate variables such as total energy density, internal energy density or entropy density. The hydrodynamic boundary conditions, which represent a generalization of the generalized Navier slip boundary condition for non-isothermal flows, are imposed in the proposed model. We then derive the dimensionless form of the model and prove that it rigorously satisfies both the first and second laws of thermodynamics. Based on the dimensionless system, an efficient numerical scheme is constructed by extending the multiple scalar auxiliary variable approach to the entropy production. The resulting scheme is decoupled, linear, unconditionally entropy-stable, and preserves mass conservation as well as the boundedness of number density at the fully discrete level. Several numerical results are presented to validate the effectiveness and stability of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114590"},"PeriodicalIF":3.8,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838828","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}
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