Journal of Computational Physics最新文献

{"title":"Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients","authors":"Hamad El Kahza ,&nbsp;Jing-Mei Qiu ,&nbsp;Luis Chacón ,&nbsp;William Taitano","doi":"10.1016/j.jcp.2025.114377","DOIUrl":"10.1016/j.jcp.2025.114377","url":null,"abstract":"<div><div>We consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For <span><math><mi>d</mi></math></span>-dimensional problems (here, <span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn></mrow></math></span> or 3), the computational complexity and memory storage of the approach are found numerically to scale as <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>N</mi><msup><mi>r</mi><mn>2</mn></msup><mo>)</mo></mrow><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msup><mi>r</mi><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>N</mi><mi>r</mi><mo>)</mo></mrow><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msup><mi>r</mi><mi>d</mi></msup><mo>)</mo></mrow></mrow></math></span>, respectively, with <span><math><mi>N</mi></math></span> the one-dimensional resolution and <span><math><mi>r</mi></math></span> the maximal rank during the Krylov iteration (which we find to be largely independent of <span><math><mi>N</mi></math></span> on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114377"},"PeriodicalIF":3.8,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157564","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":"Uncertainty and error quantification for data-driven Reynolds-averaged turbulence modelling with mean-variance estimation networks","authors":"Anthony Man,&nbsp;Mohammad Jadidi,&nbsp;Amir Keshmiri,&nbsp;Hujun Yin,&nbsp;Yasser Mahmoudi","doi":"10.1016/j.jcp.2025.114388","DOIUrl":"10.1016/j.jcp.2025.114388","url":null,"abstract":"<div><div>Amid growing interest in machine learning, numerous data-driven models have recently been developed for Reynolds-averaged turbulence modelling. However, their results generally show that they fail to give accurate predictions for test cases that have different flow phenomena to the training cases. As these models have begun to be applied to practical cases typically seen in industry such as in cooling and nuclear, improving or incorporating metrics to measure their reliability has become an important matter. To this end, a novel data-driven approach that uses mean-variance estimation networks (MVENs) is proposed in the present work. MVENs enable efficient computation as a key advantage over other uncertainty quantification (UQ) methods – during model training with maximum likelihood estimation, and UQ with a single forward propagation. Furthermore, the predicted standard deviation is also shown to be an appropriate proxy variable for the error in the mean predictions, thereby providing error quantification (EQ) capabilities. The new tensor-basis neural network with MVEN integration was compared with its popular underlying data-driven model by evaluating them on two test cases: a separated flow and a secondary flow. In both cases, the proposed approach preserved the predictive accuracy of the underlying data-driven model, while efficiently providing reliability metrics in the form of UQ and EQ. For the purposes of turbulence modelling, this work demonstrates that the UQ and EQ mechanisms in MVENs enable risk-informed predictions to be made and therefore can provide insightful reliability measures in more complex cases, such as those found in industry.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114388"},"PeriodicalIF":3.8,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145128183","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 posteriori error analysis of mixed finite element methods for a regularized μ(I)-rheology model of granular materials","authors":"Sergio Caucao ,&nbsp;Gabriel N. Gatica ,&nbsp;Saulo R. Medrado ,&nbsp;Yuri D. Sobral","doi":"10.1016/j.jcp.2025.114378","DOIUrl":"10.1016/j.jcp.2025.114378","url":null,"abstract":"<div><div>We consider a Banach spaces-based mixed variational formulation recently proposed for the stationary <span><math><mrow><mi>μ</mi><mo>(</mo><mi>I</mi><mo>)</mo></mrow></math></span>-rheology model of granular materials, and develop the first reliable and efficient residual-based <em>a posteriori</em> error estimator for its associated mixed finite element scheme in both 2D and 3D, considering PEERS and AFW-based discretizations. For the reliability analysis, and due to the nonlinear nature of the problem, we employ the first-order Gâteaux derivative of the global operator involved in the problem, combined with appropriate small-data assumptions, a stable Helmholtz decomposition in nonstandard Banach spaces, and local approximation properties of the Raviart–Thomas and Clément interpolants. In turn, inverse inequalities, the localization technique based on bubble functions in local <span><math><msup><mi>L</mi><mi>p</mi></msup></math></span>-spaces, and known results from previous works are the main tools yielding the efficiency estimate. Finally, several numerical examples confirming the theoretical properties of the estimator and illustrating the performance of the associated adaptive algorithms are reported. In particular, the case of fluid flow through a 2D cavity with two circular obstacles is considered.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114378"},"PeriodicalIF":3.8,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155863","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 artificial viscosity approach to high order entropy stable discontinuous Galerkin methods","authors":"Jesse Chan","doi":"10.1016/j.jcp.2025.114380","DOIUrl":"10.1016/j.jcp.2025.114380","url":null,"abstract":"<div><div>Entropy stable discontinuous Galerkin (DG) methods improve the robustness of high order DG simulations of nonlinear conservation laws. These methods yield a semi-discrete entropy inequality, and rely on an algebraic flux differencing formulation which involves both summation-by-parts (SBP) discretization matrices and entropy conservative two-point finite volume fluxes. However, explicit expressions for such two-point finite volume fluxes may not be available for all systems, or may be computationally expensive to compute.</div><div>This paper proposes an alternative approach to constructing entropy stable DG methods using an entropy correction artificial viscosity, where the artificial viscosity coefficient is determined based on the local violation of a cell entropy inequality and the local entropy dissipation. The resulting method is a modification of the entropy correction introduced by Abgrall, Öffner, and Ranocha in [1], and recovers the same global semi-discrete entropy inequality that is satisfied by entropy stable flux differencing DG methods. The entropy correction artificial viscosity coefficients are parameter-free and locally computable over each cell, and the resulting artificial viscosity preserves both high order accuracy and a hyperbolic maximum stable time-step size under explicit time-stepping.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114380"},"PeriodicalIF":3.8,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157561","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":"Stochastic operator learning for chemistry in non-equilibrium flows","authors":"Mridula Kuppa ,&nbsp;Roger Ghanem ,&nbsp;Marco Panesi","doi":"10.1016/j.jcp.2025.114381","DOIUrl":"10.1016/j.jcp.2025.114381","url":null,"abstract":"<div><div>This work introduces a novel framework that combines physically consistent model error characterization with spectral expansions-based operator learning for reduced-order models of non-equilibrium chemical kinetics, ultimately leading to a stochastic operator learning approach. By leveraging the Bayesian framework, we identify and infer sources of model error and parametric uncertainty within the coarse-graining methodology (CGM) across a range of initial conditions. The model error is embedded into the chemical kinetics model to ensure that its propagation to quantities of interest remains physically consistent. For operator learning, we develop a methodology that separates temporal dynamics from the parameters governing initial conditions, model error, and parametric uncertainty. Karhunen-Loève expansion (KLE) is employed to capture temporal dynamics, yielding temporal modes, while polynomial chaos expansion (PCE) is subsequently used to map model error and input parameters to the KLE coefficients. This proposed model offers three significant advantages: i) Separating the temporal dynamics from other inputs ensures the stability of the chemistry surrogate when coupled with fluid solvers; ii) The framework fully accounts for model and parametric uncertainty, enabling robust probabilistic predictions; iii) The surrogate model is highly interpretable, with visualizable temporal modes and a PCE component that facilitates the analytical calculation of sensitivity indices, allowing for the ranking of input parameter influence. We apply this framework to the <span><math><mrow><msub><mrow><mi>O</mi></mrow><mn>2</mn></msub><mspace></mspace><mo>−</mo><mspace></mspace><mrow><mi>O</mi></mrow></mrow></math></span> chemistry system under hypersonic flight conditions, validating it in both a 0-D adiabatic reactor and coupled simulations with a fluid solver in a 1-D normal shock test case. Results demonstrate that the surrogate is stable during time integration, delivers physically consistent probabilistic predictions accounting for both model and parametric uncertainty, and achieves a maximum relative error below 10 %. This work represents a significant step forward in enabling probabilistic predictions of non-equilibrium chemical kinetics within coupled fluid solvers, offering a physically accurate approach for hypersonic flow predictions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114381"},"PeriodicalIF":3.8,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157563","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":"Kalman filter-based dynamic mode decomposition for closed-loop flow control with noise-corrupted sensing","authors":"Yijia Peng ,&nbsp;Jinsheng Song ,&nbsp;Zhenlin Xie ,&nbsp;Benlong Wang ,&nbsp;Weiwei Cai ,&nbsp;Di Peng ,&nbsp;Yingzheng Liu ,&nbsp;Xin Wen","doi":"10.1016/j.jcp.2025.114386","DOIUrl":"10.1016/j.jcp.2025.114386","url":null,"abstract":"<div><div>The increasing adoption of dynamic mode decomposition with control (DMDc) in closed-loop flow control highlights a critical gap, with success in idealized conditions contrasting sharply with compromised accuracy in noise-prone scenarios. This study responds by presenting a rigorous analysis of the systematic bias induced by measurement noise and proposing the Kalman filter-based DMDc (KFDMDc) as a tailored solution. This analysis reveals the quantitative dependence of the bias on both data size and noise level, and demonstrates how noise confined to state measurements propagates nonlinearly to the control matrix. Moreover, the proposed KFDMDc algorithm directly alleviates systematic bias by employing a Kalman filter to estimate the true underlying states from noisy measurements, resulting in a significantly more accurate system identification. Numerical investigations on synthetic systems reveal a critical trade-off: the well-recognized accuracy of established diagnostic algorithms is often achieved at the expense of robustness and computational efficiency. As a result, these algorithms perform poorly when applied to time-varying controlled flow systems. In contrast, KFDMDc achieves a more favorable balance between robustness and satisfactory accuracy. The practical effectiveness of the proposed method is confirmed through closed-loop flow control simulations, achieving a <span><math><mrow><mn>22.47</mn><mrow><mo>%</mo></mrow></mrow></math></span> reduction in convergence time at low noise levels while suppressing input perturbations by <span><math><mrow><mn>74.63</mn><mrow><mo>%</mo></mrow></mrow></math></span> in high-noise regimes. Given the ubiquity of sensor noise in physical systems, the proposed KFDMDc provides a promising bridge between noise-free scenarios and the practical application of data-driven control.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114386"},"PeriodicalIF":3.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155862","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 conforming interface approach for phase transitions in rarefied gas dynamics","authors":"Donat Weniger,&nbsp;Manuel Torrilhon","doi":"10.1016/j.jcp.2025.114376","DOIUrl":"10.1016/j.jcp.2025.114376","url":null,"abstract":"<div><div>In rarefied gas dynamics, classical models like Fourier’s law cannot be used due to insufficient collisions and the lack of equilibrium. Extended gas dynamics models, such as moment approximations in kinetic theory, augment traditional continuum mechanics and include more variables and equations to describe the state of the gas, resulting in increased complexity of the equations. Similarly, the phase interface is subject to jump conditions that couple interface velocity, local equilibrium, and non-equilibrium variables in a possibly discontinuous way, triggering boundary layer effects that shape the bulk solution. Together with the nonlinear coupling of the evolving domain and the physical field equations, phase transitions in rarefied gas dynamics pose a significant challenge to numerical discretizations.</div><div>In this paper, we present a mesh-conforming interface method using standard finite elements and the level-set method with remeshing. At each time step, the domain is remeshed such that the computational mesh is conforming to the interface. This yields highly accurate and robust representations of the phase interface, allowing the interface conditions to be imposed directly and thus avoiding interpolation errors. Non-conforming methods, where an auxiliary function is used to represent the interface, lack those features.</div><div>The finite element solver and the meshing tool in our framework are exchangeable and adaptable. We provide an example implementation that is freely available and reusable in the reproducibility repository accompanying this paper. The framework is validated with simulations of the classical Stefan problem, and its flexibility is demonstrated on a model problem for rarefied gas heat conduction.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114376"},"PeriodicalIF":3.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119812","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":"Novel Monte Carlo weight window generator for global tallying problems based on maximization of global efficiency indicator","authors":"Xian Zhang ,&nbsp;Shu Li ,&nbsp;Xin Wang ,&nbsp;DanHua ShangGuan","doi":"10.1016/j.jcp.2025.114383","DOIUrl":"10.1016/j.jcp.2025.114383","url":null,"abstract":"<div><div>Weight window method is powerful in seeking precise global tallies or single target tally of particle transport problems within a reasonable time cost when its parameters are suitable. But how to get excellent parameters is not trivial, especially for complex transport models. Various strategies are proposed to set numerous parameters of this method based on various considerations. But this challenging problem is still open for new exploration despite all the progress which have been achieved. This paper aims to solve the global tallying problem, which is more difficult in the vast majority of all cases, by a novel weight window generator which supplies excellent parameters of weight window method. This generator relies on the maximization of global efficiency indicator and a natural adaptive strategy. The efficiency and reliability of this generator are validated on the Winfrith Water benchmark and AP1000 full-core model, respectively. Compared to the classical MAGIC method, this proposed method can enhance global efficiency by 2-3 times magnitude when measured by the same global efficiency indicator.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114383"},"PeriodicalIF":3.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient implicit time-marching schemes with high-order stencils for compressible flow","authors":"Zaid H. Sabri ,&nbsp;Ray Hixon","doi":"10.1016/j.jcp.2025.114360","DOIUrl":"10.1016/j.jcp.2025.114360","url":null,"abstract":"<div><div>Time-marching techniques are a cornerstone of Computational Aeroacoustics, but existing approaches face significant challenges. Explicit schemes, though straightforward, often require excessively small time steps to maintain numerical stability, while traditional implicit methods achieve larger time steps at the cost of high computational expense per step. This research presents a novel implicit framework that combines high-order differencing stencils for enhanced physical accuracy with low-order preconditioning to ensure numerical stability and efficiency. A comprehensive stability analysis is conducted for preconditioned implicit formulations in both inviscid and viscous flow regimes. The framework is validated across a range of benchmark problems, including one-dimensional, two-dimensional, and three-dimensional inviscid compressible flows, as well as a one-dimensional viscous problem. Results demonstrate the scheme’s ability to achieve robust stability, high accuracy, and reduced computational overhead compared to traditional implicit methods, making it a promising approach for high-fidelity aeroacoustic simulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114360"},"PeriodicalIF":3.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145128182","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":"Consistent multiple-relaxation-time lattice Boltzmann method for the volume-averaged Navier-Stokes equations","authors":"Yang Liu ,&nbsp;Xuan Zhang ,&nbsp;Jingchun Min ,&nbsp;Xiaomin Wu","doi":"10.1016/j.jcp.2025.114379","DOIUrl":"10.1016/j.jcp.2025.114379","url":null,"abstract":"<div><div>The volume-averaged Navier-Stokes equations (VANSE), serving as the cornerstone of various fluid-solid multiphase models, have recently been reported to be solved using a pressure-based lattice Boltzmann (LB) method that decouples the pressure from density and exhibits good numerical performance [<span><span>1</span></span>]. However, the widely adopted density-based LB scheme still suffers from significant spurious velocities and inconsistency with VANSE. To remedy this issue, this paper introduces a multiple-relaxation-time LB method, which incorporates a provisional equation of state into the redefined equilibrium distribution to decouple the void fraction from density, and readjusts a correction force to produce correct pressure term. Also, Galilean invariance of the recovered VANSE is guaranteed by devising a source term in moment space, effectively eliminating unwanted numerical errors in viscous stress tensor. Through Chapman-Enskog analysis and comprehensive numerical validations, this proposed scheme is demonstrated to be capable of recovering consistent VANSE with second-order accuracy, and offers better numerical stability over previous schemes for handling void fraction fields with large gradients and spatiotemporal distributions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114379"},"PeriodicalIF":3.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097582","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}