Pub Date : 2026-05-15Epub Date: 2026-02-02DOI: 10.1016/j.jcp.2026.114729
Yaqing Yang , Fengxiang Zhao , Kun Xu
A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged derivatives to introduce additional degrees of freedom, enabling a compact stencil with superior resolution. For non-orthogonal meshes, reconstruction is performed on a standard reference cell in a transformed computational space. This approach provides a unified polynomial form, significantly reducing memory usage and computational cost while simplifying implementation compared to direct multi-dimensional or dimension-by-dimension methods. A nonlinear adaptive method ensures high accuracy and robustness by smoothly transitioning from the high-order linear scheme in smooth regions to a second-order scheme at discontinuities. The method is implemented with multi-GPU parallelization using CUDA and MPI for large-scale applications. Comprehensive numerical tests, from subsonic to supersonic turbulence, validate the scheme’s high accuracy, resolution and excellent robustness.
{"title":"An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows","authors":"Yaqing Yang , Fengxiang Zhao , Kun Xu","doi":"10.1016/j.jcp.2026.114729","DOIUrl":"10.1016/j.jcp.2026.114729","url":null,"abstract":"<div><div>A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged derivatives to introduce additional degrees of freedom, enabling a compact stencil with superior resolution. For non-orthogonal meshes, reconstruction is performed on a standard reference cell in a transformed computational space. This approach provides a unified polynomial form, significantly reducing memory usage and computational cost while simplifying implementation compared to direct multi-dimensional or dimension-by-dimension methods. A nonlinear adaptive method ensures high accuracy and robustness by smoothly transitioning from the high-order linear scheme in smooth regions to a second-order scheme at discontinuities. The method is implemented with multi-GPU parallelization using CUDA and MPI for large-scale applications. Comprehensive numerical tests, from subsonic to supersonic turbulence, validate the scheme’s high accuracy, resolution and excellent robustness.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114729"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186550","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 : 2026-05-15Epub Date: 2026-01-31DOI: 10.1016/j.jcp.2026.114723
Hongji Wang , Hongqiao Wang , Jinyong Ying , Qingping Zhou
Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, the Darcy flow equation is a fundamental equation in fluid mechanics, which plays a crucial role in understanding fluid flow through porous media. Bayesian methods provide an effective approach for solving PDE inverse problems, while their numerical implementation requires numerous evaluations of computationally expensive forward solvers. Therefore, the adoption of surrogate models with lower computational costs is essential. However, constructing a globally accurate surrogate model for high-dimensional complex problems demands high model capacity and large amounts of data. To address this challenge, this study proposes an efficient locally accurate surrogate that focuses on the high-probability regions of the true likelihood in inverse problems, with relatively low model complexity and few training data requirements. Additionally, we introduce a sequential Bayesian design strategy to acquire the proposed surrogate since the high-probability region of the likelihood is unknown. The strategy treats the posterior evolution process of sequential Bayesian design as a Gaussian process, enabling algorithmic acceleration through one-step ahead prior. The complete algorithmic framework is referred to as sequential Bayesian design for locally accurate surrogate (SBD-LAS). Finally, three experiments based on the Darcy flow equation demonstrate the advantages of the proposed method in terms of both inversion accuracy and computational speed.
{"title":"Sequential Bayesian design for efficient surrogate construction in the inversion of Darcy flows","authors":"Hongji Wang , Hongqiao Wang , Jinyong Ying , Qingping Zhou","doi":"10.1016/j.jcp.2026.114723","DOIUrl":"10.1016/j.jcp.2026.114723","url":null,"abstract":"<div><div>Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, the Darcy flow equation is a fundamental equation in fluid mechanics, which plays a crucial role in understanding fluid flow through porous media. Bayesian methods provide an effective approach for solving PDE inverse problems, while their numerical implementation requires numerous evaluations of computationally expensive forward solvers. Therefore, the adoption of surrogate models with lower computational costs is essential. However, constructing a globally accurate surrogate model for high-dimensional complex problems demands high model capacity and large amounts of data. To address this challenge, this study proposes an efficient locally accurate surrogate that focuses on the high-probability regions of the true likelihood in inverse problems, with relatively low model complexity and few training data requirements. Additionally, we introduce a sequential Bayesian design strategy to acquire the proposed surrogate since the high-probability region of the likelihood is unknown. The strategy treats the posterior evolution process of sequential Bayesian design as a Gaussian process, enabling algorithmic acceleration through <em>one-step ahead prior</em>. The complete algorithmic framework is referred to as sequential Bayesian design for locally accurate surrogate (SBD-LAS). Finally, three experiments based on the Darcy flow equation demonstrate the advantages of the proposed method in terms of both inversion accuracy and computational speed.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114723"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186548","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 : 2026-05-15Epub Date: 2026-01-31DOI: 10.1016/j.jcp.2026.114725
Deniz Günseren , Özgür Ertunç , Ismail Ari , Atakan Ataman Atik , Nitel Muhtaroglu , Ivan Otić
This study develops a neural network (NN) model to predict the decay of homogeneous isotropic turbulence (HIT). A series of decay cases was simulated using a GPU-accelerated pseudo-spectral solver over a low range of Taylor-scale Reynolds numbers, and the resulting time-resolved fields were converted to dimensionless form and used as training and validation data. A central contribution of this work is a fully dimensionless and Reynolds-number–consistent formulation of the HIT decay equations, which allows the decay coefficient to be identified directly from data. Traditional decay models often combine available experimental or numerical data with asymptotic descriptions of turbulence behavior in the limits Reλ → 0 and Reλ → ∞; however, such asymptotic guidance may rely on mathematically inconsistent relationships. By pairing the consistent nondimensional formulation with reliable DNS data, we obtain a data-driven decay function Z that reflects the governing dynamics across the simulated Reynolds-number range. A physics-informed neural network (PINN) is then trained to model the evolution of the normalized velocity and dissipation fields. Held-out cases demonstrate accurate prediction of key turbulence quantities together with an explicit, data-inferred closure for turbulence decay.
{"title":"Constructing a reynolds stress model of decaying homogeneous isotropic turbulence using physics informed neural network","authors":"Deniz Günseren , Özgür Ertunç , Ismail Ari , Atakan Ataman Atik , Nitel Muhtaroglu , Ivan Otić","doi":"10.1016/j.jcp.2026.114725","DOIUrl":"10.1016/j.jcp.2026.114725","url":null,"abstract":"<div><div>This study develops a neural network (NN) model to predict the decay of homogeneous isotropic turbulence (HIT). A series of decay cases was simulated using a GPU-accelerated pseudo-spectral solver over a low range of Taylor-scale Reynolds numbers, and the resulting time-resolved fields were converted to dimensionless form and used as training and validation data. A central contribution of this work is a fully dimensionless and Reynolds-number–consistent formulation of the HIT decay equations, which allows the decay coefficient to be identified directly from data. Traditional decay models often combine available experimental or numerical data with asymptotic descriptions of turbulence behavior in the limits <em>Re<sub>λ</sub></em> → 0 and <em>Re<sub>λ</sub></em> → ∞; however, such asymptotic guidance may rely on mathematically inconsistent relationships. By pairing the consistent nondimensional formulation with reliable DNS data, we obtain a data-driven decay function <em>Z</em> that reflects the governing dynamics across the simulated Reynolds-number range. A physics-informed neural network (PINN) is then trained to model the evolution of the normalized velocity and dissipation fields. Held-out cases demonstrate accurate prediction of key turbulence quantities together with an explicit, data-inferred closure for turbulence decay.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114725"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186545","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 develop a novel class of high-order structure-preserving algorithms for simulating the Schrödinger–Poisson–Slater system. We rewrite the original Schrödinger–Poisson–Slater system into equivalent formulas which warrant exactly the original total mass and energy. Based on the new formulas, a new family of high-order, mass and energy conserving schemes is constructed. We also show that the structure-preserving schemes can be proved to be uniquely solved. Extensive numerical examples in 2D and 3D are provided to demonstrate the high-order convergence rate and the effectiveness of the proposed algorithm in conserving mass and energy. Compared with the existing non-conserved schemes, the advantage of our schemes is that the structure-preserving schemes can also significantly reduce the errors of the numerical solutions in long-time simulations.
{"title":"High-order structure-preserving schemes for the Schrödinger–Poisson–Slater system","authors":"Qing Cheng , Xiaoyun Jiang , Zongze Yang , Hui Zhang","doi":"10.1016/j.jcp.2026.114715","DOIUrl":"10.1016/j.jcp.2026.114715","url":null,"abstract":"<div><div>In this paper, we develop a novel class of high-order structure-preserving algorithms for simulating the Schrödinger–Poisson–Slater system. We rewrite the original Schrödinger–Poisson–Slater system into equivalent formulas which warrant exactly the original total mass and energy. Based on the new formulas, a new family of high-order, mass and energy conserving schemes is constructed. We also show that the structure-preserving schemes can be proved to be uniquely solved. Extensive numerical examples in 2D and 3D are provided to demonstrate the high-order convergence rate and the effectiveness of the proposed algorithm in conserving mass and energy. Compared with the existing non-conserved schemes, the advantage of our schemes is that the structure-preserving schemes can also significantly reduce the errors of the numerical solutions in long-time simulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114715"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098802","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 : 2026-05-15Epub Date: 2026-01-29DOI: 10.1016/j.jcp.2026.114718
Kevin Gill , Ionuţ-Gabriel Farcaş , Silke Glas , Benjamin J. Faber
Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and uncertainty quantification, are essential for developing digital twins in real-world applications. However, standard grid-based data generation methods are computationally prohibitive due to the curse of dimensionality, as their cost scales exponentially with the number of inputs. This paper investigates efficient training of parametric data-driven ROMs using sparse grid interpolation with (L)-Leja points, specifically targeting scenarios with higher-dimensional input parameter spaces. (L)-Leja points are nested and exhibit slow growth, resulting in sparse grids with low cardinality in low-to-medium dimensional settings, making them ideal for large-scale, computationally expensive problems. Focusing on gyrokinetic simulations of plasma micro-instabilities in fusion experiments as a representative real-world application, we construct parametric ROMs for the full 5D gyrokinetic distribution function via optimized dynamic mode decomposition (optDMD) and sparse grids based on (L)-Leja points. We perform detailed experiments in two scenarios: First, the Cyclone Base Case benchmark assesses optDMD ROM prediction capabilities beyond training time horizons and across variations in the binormal wave number. Second, for a real-world electron-temperature-gradient-driven micro-instability simulation with six input parameters, we demonstrate that a predictive parametric optDMD ROM that is up to three orders of magnitude cheaper to evaluate can be constructed using only 28 high-fidelity gyrokinetic simulations, enabled by the use of sparse grids. In the broader context of fusion research, these results demonstrate the potential of sparse grid-based parametric ROMs to enable otherwise intractable many-query tasks.
在大量输入参数中嵌入依赖关系的参数化数据驱动降阶模型（ROMs）对于在大规模问题中实现多查询任务至关重要。这些任务，包括设计优化、控制和不确定性量化，对于在实际应用中开发数字孪生至关重要。然而，由于维度的诅咒，标准的基于网格的数据生成方法在计算上是令人望而却步的，因为它们的成本随着输入的数量呈指数级增长。本文研究了使用(L)-Leja点的稀疏网格插值对参数数据驱动rom的有效训练，特别是针对具有高维输入参数空间的场景。(L)-Leja点嵌套且增长缓慢，导致在中低维设置中具有低基数的稀疏网格，使其成为大规模，计算成本高的问题的理想选择。以聚变实验中等离子体微不稳定性的陀螺动力学模拟为代表的现实世界应用，我们通过优化动态模式分解（optDMD）和基于(L)-Leja点的稀疏网格构建了全5D陀螺动力学分布函数的参数rom。我们在两种情况下进行了详细的实验：首先，Cyclone Base Case基准评估了超越训练时间范围和双正态波数变化的optDMD ROM预测能力。其次，对于具有六个输入参数的真实电子温度梯度驱动的微不稳定性模拟，我们证明了仅使用28个高保真陀螺仪动力学模拟就可以构建一个预测参数optDMD ROM，其评估成本降低了三个数量级。在更广泛的融合研究背景下，这些结果证明了基于稀疏网格的参数rom的潜力，可以实现其他难以处理的多查询任务。
{"title":"Fast prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition","authors":"Kevin Gill , Ionuţ-Gabriel Farcaş , Silke Glas , Benjamin J. Faber","doi":"10.1016/j.jcp.2026.114718","DOIUrl":"10.1016/j.jcp.2026.114718","url":null,"abstract":"<div><div>Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and uncertainty quantification, are essential for developing digital twins in real-world applications. However, standard grid-based data generation methods are computationally prohibitive due to the curse of dimensionality, as their cost scales exponentially with the number of inputs. This paper investigates efficient training of parametric data-driven ROMs using sparse grid interpolation with (<em>L</em>)-Leja points, specifically targeting scenarios with higher-dimensional input parameter spaces. (<em>L</em>)-Leja points are nested and exhibit slow growth, resulting in sparse grids with low cardinality in low-to-medium dimensional settings, making them ideal for large-scale, computationally expensive problems. Focusing on gyrokinetic simulations of plasma micro-instabilities in fusion experiments as a representative real-world application, we construct parametric ROMs for the full 5D gyrokinetic distribution function via optimized dynamic mode decomposition (optDMD) and sparse grids based on (<em>L</em>)-Leja points. We perform detailed experiments in two scenarios: First, the Cyclone Base Case benchmark assesses optDMD ROM prediction capabilities beyond training time horizons and across variations in the binormal wave number. Second, for a real-world electron-temperature-gradient-driven micro-instability simulation with six input parameters, we demonstrate that a predictive parametric optDMD ROM that is up to three orders of magnitude cheaper to evaluate can be constructed using only 28 high-fidelity gyrokinetic simulations, enabled by the use of sparse grids. In the broader context of fusion research, these results demonstrate the potential of sparse grid-based parametric ROMs to enable otherwise intractable many-query tasks.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114718"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098785","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 : 2026-05-15Epub Date: 2026-01-31DOI: 10.1016/j.jcp.2026.114724
Fan Zhang , Andrea Lani , Stefaan Poedts
Approximate Riemann solvers are widely used for solving hyperbolic conservation laws, including those of magnetohydrodynamics (MHD). However, due to the nonlinearity and complexity of MHD, obtaining accurate and robust numerical solutions to MHD equations is non-trivial, and it may be challenging for an approximate MHD Riemann solver to preserve the positivity of scalar variables, particularly when the plasma β is low. As we have identified that the inconsistency between the numerically calculated magnetic field and magnetic energy may be at least partly responsible for the loss of positivity of scalar variables, we propose a consistency condition for calculating the intermediate energies within the Riemann fan and implement it in HLL-type MHD Riemann solvers, thereby alleviating erroneous magnetic field solutions that break scalar positivity. In addition, (I) for the HLLC-type scheme, we have designed a revised two-state approximation, specifically reducing numerical error in magnetic field solutions, although sacrificing the contact-resolving capability, and (II) for the HLLD-type scheme, we replace the constant total pressure assumption by a three-state assumption for the intermediate thermal energy, which is more consistent with our other assumptions. The proposed schemes perform better in numerical examples with low plasma β. Moreover, we explained the energy error introduced during time integration.
{"title":"On energy consistency of intermediate states in HLL-type MHD Riemann solvers","authors":"Fan Zhang , Andrea Lani , Stefaan Poedts","doi":"10.1016/j.jcp.2026.114724","DOIUrl":"10.1016/j.jcp.2026.114724","url":null,"abstract":"<div><div>Approximate Riemann solvers are widely used for solving hyperbolic conservation laws, including those of magnetohydrodynamics (MHD). However, due to the nonlinearity and complexity of MHD, obtaining accurate and robust numerical solutions to MHD equations is non-trivial, and it may be challenging for an approximate MHD Riemann solver to preserve the positivity of scalar variables, particularly when the plasma <em>β</em> is low. As we have identified that the inconsistency between the numerically calculated magnetic field and magnetic energy may be at least partly responsible for the loss of positivity of scalar variables, we propose a consistency condition for calculating the intermediate energies within the Riemann fan and implement it in HLL-type MHD Riemann solvers, thereby alleviating erroneous magnetic field solutions that break scalar positivity. In addition, (I) for the HLLC-type scheme, we have designed a revised two-state approximation, specifically reducing numerical error in magnetic field solutions, although sacrificing the contact-resolving capability, and (II) for the HLLD-type scheme, we replace the constant total pressure assumption by a three-state assumption for the intermediate thermal energy, which is more consistent with our other assumptions. The proposed schemes perform better in numerical examples with low plasma <em>β</em>. Moreover, we explained the energy error introduced during time integration.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114724"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186543","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 : 2026-05-15Epub Date: 2026-01-31DOI: 10.1016/j.jcp.2026.114720
Cheng Wang , Yi Liang , Pengtao Sun , Yan Chen , Jiarui Han
In this paper, an energy-stable monolithic interface-fitted/fictitious domain-finite element method (MIF/FD-FEM) is developed for solving fluid-rigid body interaction problems, where the rigid body may undergo large displacements. Different from the classical arbitrary Lagrangian-Eulerian (ALE) method for FSI problems, the proposed numerical method utilizes the ALE technique within the frame of fictitious domain method to numerically deal with the constrain in the interface condition of continuous velocity across the interface of the fluid and rigid body, and thus can reduce or even avoid the use of remeshing-interpolation technique when large displacements of rigid bodies occur. Meanwhile, the interface-fitted mesh can be constructed from the previously unfitted mesh by locally moving mesh nodes near the interface to make the mesh fit the interface. In particular, the proposed numerical scheme is developed in a monolithic fashion for fluid-rigid body interaction problems by constructing a specific finite element space and associated basis functions, where although some basis functions are not standard finite element’s nodal shape functions, the corresponding algebraic system can still be generated by means of standard finite element computations with some modifications on elemental matrices and elemental vectors. Moreover, it is verified that the developed novel MIF/FD-FEM can preserve the energy-dissipating property along the time, which ensures a strong energy stability for a long term FSI simulation. Numerical experiments are conducted to validate the effectiveness, accuracy and energy stability/dissipation of the developed MIF/FD-FEM by applying it to a benchmark example of fluid-rigid body interaction problem, an example of lid-driven cavity flow and an example arising from the deterministic lateral displacement (DLD) problem for particle separations, where its superiority over the partitioned/decoupled scheme is investigated as well.
{"title":"An energy-stable monolithic interface-fitted/fictitious domain-finite element method for interaction problems of fluid and rigid body with large displacements","authors":"Cheng Wang , Yi Liang , Pengtao Sun , Yan Chen , Jiarui Han","doi":"10.1016/j.jcp.2026.114720","DOIUrl":"10.1016/j.jcp.2026.114720","url":null,"abstract":"<div><div>In this paper, an energy-stable monolithic interface-fitted/fictitious domain-finite element method (MIF/FD-FEM) is developed for solving fluid-rigid body interaction problems, where the rigid body may undergo large displacements. Different from the classical arbitrary Lagrangian-Eulerian (ALE) method for FSI problems, the proposed numerical method utilizes the ALE technique within the frame of fictitious domain method to numerically deal with the constrain in the interface condition of continuous velocity across the interface of the fluid and rigid body, and thus can reduce or even avoid the use of remeshing-interpolation technique when large displacements of rigid bodies occur. Meanwhile, the interface-fitted mesh can be constructed from the previously unfitted mesh by locally moving mesh nodes near the interface to make the mesh fit the interface. In particular, the proposed numerical scheme is developed in a monolithic fashion for fluid-rigid body interaction problems by constructing a specific finite element space and associated basis functions, where although some basis functions are not standard finite element’s nodal shape functions, the corresponding algebraic system can still be generated by means of standard finite element computations with some modifications on elemental matrices and elemental vectors. Moreover, it is verified that the developed novel MIF/FD-FEM can preserve the energy-dissipating property along the time, which ensures a strong energy stability for a long term FSI simulation. Numerical experiments are conducted to validate the effectiveness, accuracy and energy stability/dissipation of the developed MIF/FD-FEM by applying it to a benchmark example of fluid-rigid body interaction problem, an example of lid-driven cavity flow and an example arising from the deterministic lateral displacement (DLD) problem for particle separations, where its superiority over the partitioned/decoupled scheme is investigated as well.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114720"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186470","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 : 2026-05-15Epub Date: 2026-01-27DOI: 10.1016/j.jcp.2026.114711
Mario Álvarez , Eligio Colmenares , Filánder A. Sequeira
This work extends a previous study of ours, established in [M. Álvarez et al., Comput. Math. Appl., 114(2021), 112–131], on a semi-augmented mixed finite element formulation for double-diffusive natural convection in porous media, by developing and analyzing a new augmented fully mixed scheme in both two and three spatial dimensions. The formulation introduces a tensorial pseudo-thermosolutal gradient, depending on the gradients of temperature and concentration, as an additional unknown. This enrichment leads to a mixed system for the coupled equations and brings several computational advantages: the gradients of temperature and concentration can be efficiently recovered from the discrete solution without loss of accuracy; Dirichlet boundary conditions are incorporated naturally, without the need for Lagrange multipliers or extension operators; and the incorporation of parameterized redundant Galerkin terms ensures coercivity and allows the application of the Lax-Milgram theorem, thereby removing the need for inf-sup compatibility conditions and enabling greater flexibility in the selection of finite element subspaces. The scheme admits finite element spaces of arbitrary polynomial degree and achieves optimal-order convergence rates, established through both a priori and a posteriori error analyses. We also propose two computable residual-based a posteriori error estimators, which are entirely local and avoid the nonlocal norms required in previous approaches. These theoretical results are further supported by adaptive numerical experiments in two dimensions, which confirm the efficiency and reliability of the method.
{"title":"Adaptive computation driven by an augmented fully-mixed FEM for double-diffusive natural convection in porous media","authors":"Mario Álvarez , Eligio Colmenares , Filánder A. Sequeira","doi":"10.1016/j.jcp.2026.114711","DOIUrl":"10.1016/j.jcp.2026.114711","url":null,"abstract":"<div><div>This work extends a previous study of ours, established in [M. Álvarez <em>et al.</em>, Comput. Math. Appl., 114(2021), 112–131], on a semi-augmented mixed finite element formulation for double-diffusive natural convection in porous media, by developing and analyzing a new augmented fully mixed scheme in both two and three spatial dimensions. The formulation introduces a tensorial pseudo-thermosolutal gradient, depending on the gradients of temperature and concentration, as an additional unknown. This enrichment leads to a mixed system for the coupled equations and brings several computational advantages: the gradients of temperature and concentration can be efficiently recovered from the discrete solution without loss of accuracy; Dirichlet boundary conditions are incorporated naturally, without the need for Lagrange multipliers or extension operators; and the incorporation of parameterized redundant Galerkin terms ensures coercivity and allows the application of the Lax-Milgram theorem, thereby removing the need for inf-sup compatibility conditions and enabling greater flexibility in the selection of finite element subspaces. The scheme admits finite element spaces of arbitrary polynomial degree and achieves optimal-order convergence rates, established through both <em>a priori</em> and <em>a posteriori</em> error analyses. We also propose two computable residual-based <em>a posteriori</em> error estimators, which are entirely local and avoid the nonlocal norms required in previous approaches. These theoretical results are further supported by adaptive numerical experiments in two dimensions, which confirm the efficiency and reliability of the method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114711"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098801","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 : 2026-05-15Epub Date: 2026-02-02DOI: 10.1016/j.jcp.2026.114727
Yanling Lu, Dunhui Xiao, Rui Fu, Xuejun Xu, Shuyu Sun
This paper presents a new non-intrusive reduced order model: mesh-reduction reduced-order model (MRROM) that is based on a finite element inspired graph auto-encoder neural network and spatiotemporal graph embedding transformer (SGET) to enable stable long time fluid dynamic prediction. In particular, the model consists of two key components: the first is a newly presented finite element inspired graph auto-encoder, which employs domain decomposition topology-aware pooling to preserve the hierarchical spatial structure of the computational mesh and finite element-inspired global-aware message passing to enhance the representation of multi-scale spatial structure information of the fluid dynamics during dimensionality reduction. The second component is a spatiotemporal graph embedding transformer (SGET), which combines graph neural network (GNN)-based local spatial modeling with Transformer-based mechanisms to capture long-range temporal dependencies. Together, these components significantly enhance the model’s stability, computational efficiency, and accuracy in long-term flow dynamic prediction.
This MRROM is evaluated using three fluid flow cases: flow past a cylinder, backward-facing step flow, and two-phase bubble columns. The MRROM demonstrates the ability to learn topological structures of non-uniform meshes and dynamic evolution patterns of physical systems, achieving high-quality long-term fluid dynamics prediction.
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Pub Date : 2026-05-15Epub Date: 2026-02-03DOI: 10.1016/j.jcp.2026.114743
David J. Silvester
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing the probability of observing a bifurcated solution. The computational procedure is demonstrably robust and does not require parameter tuning. The essential feature of the strategy is that the computational solution of the Navier–Stokes equations is a reliable proxy for laboratory experiments investigating sensitivity to flow parameters. The applicability of our probabilistic bifurcation detection strategy is demonstrated by an investigation of two classical examples of flow instability associated with thermal convection. The codes used to generate and process the labelled data are available on GitHub.
{"title":"Machine learning for hydrodynamic stability","authors":"David J. Silvester","doi":"10.1016/j.jcp.2026.114743","DOIUrl":"10.1016/j.jcp.2026.114743","url":null,"abstract":"<div><div>A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing the probability of observing a bifurcated solution. The computational procedure is demonstrably robust and does not require parameter tuning. The essential feature of the strategy is that the computational solution of the Navier–Stokes equations is a reliable proxy for laboratory experiments investigating sensitivity to flow parameters. The applicability of our probabilistic bifurcation detection strategy is demonstrated by an investigation of two classical examples of flow instability associated with thermal convection. The codes used to generate and process the labelled data are available on GitHub.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114743"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186473","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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