Journal of Computational Physics最新文献

{"title":"Logarithmic mean approximation in improving entropy conservation in KEEP scheme with pressure equilibrium preservation property for compressible flows","authors":"Shigetaka Kawai,&nbsp;Soshi Kawai","doi":"10.1016/j.jcp.2025.113897","DOIUrl":"10.1016/j.jcp.2025.113897","url":null,"abstract":"<div><div>This study develops non-dissipative and robust spatial discretizations in kinetic-energy and entropy preserving (KEEP) schemes by improving the entropy conservation property, while maintaining the pressure-equilibrium-preservation (PEP) property. A main focus of this study is the approximation of the logarithmic mean, involved in the entropy-conservative numerical fluxes in the mass and energy equations. To seek suitable approximations of the logarithmic mean with the KEEP and PEP properties, we first derive the PEP condition for general entropy-conservative numerical fluxes. Then, we evaluate the entropy conservation errors for different approximations of the logarithmic mean. The present theoretical analyses reveal that the use of the geometric mean improves the entropy conservation error better than the other means. Given this theoretical result, we derive an asymptotic expansion of the logarithmic mean based on the geometric mean, which yields a smaller entropy conservation error than the existing expansions based on the arithmetic mean at each truncation order. Numerical experiments for one-dimensional density wave advection, two-dimensional isentropic vortex, three-dimensional compressible inviscid Taylor–Green vortex, and stationary normal shock demonstrate the validity of the present theoretical analyses.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"530 ","pages":"Article 113897"},"PeriodicalIF":3.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical model and numerical discretization for the simulation of two-material two-temperature compressible flows","authors":"Jian Cheng ,&nbsp;Fan Zhang","doi":"10.1016/j.jcp.2025.113896","DOIUrl":"10.1016/j.jcp.2025.113896","url":null,"abstract":"<div><div>In this work, we investigate the mathematical model and the numerical method for two-material two-temperature compressible flows based on the Eulerian framework. First, we present the two-material two-temperature model equations with its basic mathematical properties. In particular, in order to close the model equations, three different closure laws and the corresponding properties related to well-posedness are discussed in detail. Then, a Weighted Essentially Non-Oscillatory (WENO) finite volume discretization is developed for the discretization of the model equations on both planar geometry and spherical axisymmetric geometry. More importantly, aiming at revealing the underlying reasons for the occurrence of spurious numerical oscillations near the material interface, a theoretical analysis of the numerical discretization coupled with the three different closure laws is carried out. Finally, a variety of typical test cases are presented to illustrate the performance of the numerical method for the proposed model equations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113896"},"PeriodicalIF":3.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519001","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":"High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations","authors":"Tarik Dzanic ,&nbsp;Luigi Martinelli","doi":"10.1016/j.jcp.2025.113895","DOIUrl":"10.1016/j.jcp.2025.113895","url":null,"abstract":"<div><div>The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. These solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113895"},"PeriodicalIF":3.8,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tensor-train WENO scheme for compressible flows","authors":"M. Engin Danis,&nbsp;Duc Truong,&nbsp;Ismael Boureima,&nbsp;Oleg Korobkin,&nbsp;Kim Ø. Rasmussen,&nbsp;Boian S. Alexandrov","doi":"10.1016/j.jcp.2025.113891","DOIUrl":"10.1016/j.jcp.2025.113891","url":null,"abstract":"<div><div>In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce <em>LF-cross</em> and <em>WENO-cross</em> methods to compute numerical fluxes and the WENO reconstruction using the cross interpolation technique. A tensor-train approach is developed for boundary condition types commonly encountered in Computational Fluid Dynamics (CFD). The performance of the proposed WENO-TT solver is investigated in a rich set of numerical experiments. We demonstrate that the WENO-TT method achieves the theoretical <span><math><msup><mrow><mtext>5</mtext></mrow><mrow><mtext>th</mtext></mrow></msup></math></span>-order accuracy of the classical WENO scheme in smooth problems while successfully capturing complicated shock structures. In an effort to avoid the growth of TT ranks, we propose a dynamic method to estimate the TT approximation error that governs the ranks and overall truncation error of the WENO-TT scheme. Finally, we show that the traditional WENO scheme can be accelerated up to 1000 times in the TT format, and the memory requirements can be significantly decreased for low-rank problems, demonstrating the potential of tensor-train approach for future CFD application. This paper is the first study that develops a finite difference WENO scheme using the tensor-train approach for compressible flows. It is also the first comprehensive work that provides a detailed perspective into the relationship between rank, truncation error, and the TT approximation error for compressible WENO solvers.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113891"},"PeriodicalIF":3.8,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep reinforcement cross-domain transfer learning of active flow control for three-dimensional bluff body flow","authors":"Lei Yan ,&nbsp;Qiulei Wang ,&nbsp;Gang Hu ,&nbsp;Wenli Chen ,&nbsp;Bernd R. Noack","doi":"10.1016/j.jcp.2025.113893","DOIUrl":"10.1016/j.jcp.2025.113893","url":null,"abstract":"<div><div>This paper applies mutual information-based knowledge transfer learning with soft actor-critic (MIKT-SAC) algorithm to address cross-domain issues in state and action dimensions for active flow control (AFC). It explores the potential of deep reinforcement learning (DRL) in discovering novel drag reduction strategies. The algorithm starts with a pretrained agent on a two-dimensional (2D) case, extracting knowledge to mitigate aerodynamic forces acting on a 3D bluff body under high Reynolds number flow conditions. The algorithm is applied to two test cases to demonstrate its capabilities and limits: The first investigates the state dimension mismatch problem using a 3D square cylinder at high Reynolds number <span><math><mi>R</mi><mi>e</mi><mo>=</mo><mn>22000</mn></math></span>, where four jets at the corners of square cylinder as actuators. The second test examines scenarios with both state and action dimension mismatches using a circular cylinder with multiple zero-net-mass-flux jets positioned as two slots on the top and bottom surfaces. The results show that MIKT-SAC method outperforms the vanilla SAC algorithm, significantly reducing 51.1% and 45.1% training time and reducing drag coefficients (<span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span>) by 50.9% and 49.4% for the square and circular cylinders, respectively, while effectively suppressing drag and lift fluctuations. The multi-jet actuation delays vortex shedding on the surface of bluff body, reducing fluctuating lift forces on both cases. These findings highlight the potential of DRL in active flow control, laying a foundation for efficient, robust, and practical implementation of bluff body control technologies in practical engineering applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113893"},"PeriodicalIF":3.8,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-splitting Eulerian-Lagrangian WENO schemes for two-dimensional nonlinear convection-diffusion equations","authors":"Nanyi Zheng ,&nbsp;Xiaofeng Cai ,&nbsp;Jing-Mei Qiu ,&nbsp;Jianxian Qiu","doi":"10.1016/j.jcp.2025.113890","DOIUrl":"10.1016/j.jcp.2025.113890","url":null,"abstract":"<div><div>In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed EL-RK-FV-WENO scheme defines modified characteristic lines and evolves the solution along them, significantly relaxing the time-step constraint for the convection term. The main algorithm design challenge arises from the complexity of constructing accurate and robust reconstructions on dynamically varying Lagrangian meshes. This reconstruction process is needed for flux evaluations on time-dependent upstream quadrilaterals and time integrations along moving characteristics. To address this, we propose a strategy that utilizes a WENO reconstruction on a fixed Eulerian mesh for spatial reconstruction, and updates intermediate solutions on the Eulerian background mesh for implicit-explicit RK temporal integration. This strategy leverages efficient reconstruction and remapping algorithms to manage the complexities of polynomial reconstructions on time-dependent quadrilaterals, while ensuring local mass conservation. The proposed scheme ensures mass conservation due to the flux-form semi-discretization and the mass-conservative reconstruction on both background and upstream cells. Extensive numerical tests have been performed to verify the effectiveness of the proposed scheme.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113890"},"PeriodicalIF":3.8,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511376","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 efficient compact splitting Fourier spectral method for computing the dynamics of rotating spin-orbit coupled spin-1 Bose-Einstein condensates","authors":"Xin Liu ,&nbsp;Yongjun Yuan ,&nbsp;Yong Zhang","doi":"10.1016/j.jcp.2025.113892","DOIUrl":"10.1016/j.jcp.2025.113892","url":null,"abstract":"<div><div>This paper focuses on the dynamic simulation of spin-1 Bose-Einstein condensates (BECs) with rotation and spin-orbit coupling (SOC), and presents a high-order compact splitting Fourier spectral method with favorable numerical properties. The Hamiltonian is split into a linear part, which consists of the Laplace, rotation and SOC terms, and a nonlinear part that includes all the remaining terms. The wave function is well approximated by the Fourier spectral method and is numerically accessed with discrete Fast Fourier transform (FFT). For the linear subproblem, we rotate the wave function by a function-rotation mapping, which is realized easily with purely FFT achieving almost optimal efficiency. The rotation term vanishes, but the SOC term becomes time-dependent. Using a time-dependent matrix decomposition and the function-rotation mapping, we can integrate the linear subproblem exactly and explicitly. The nonlinear subproblem is integrated analytically in physical space. Such “compact” splitting involves only two operators and facilitates the design of high-order splitting schemes. Our method is spectrally accurate in space and high order in time. It is efficient, explicit, unconditionally stable and simple to implement. In addition, we derive some dynamical properties and carry out a systematic study, including accuracy and efficiency tests, dynamical property verification, the SOC effects and dynamics of quantized vortices.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113892"},"PeriodicalIF":3.8,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511375","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":"Asymptotic-preserving IMEX schemes for the Euler equations of non-ideal gases","authors":"Giuseppe Orlando ,&nbsp;Luca Bonaventura","doi":"10.1016/j.jcp.2025.113889","DOIUrl":"10.1016/j.jcp.2025.113889","url":null,"abstract":"<div><div>We analyze schemes based on a general Implicit-Explicit (IMEX) time discretization for the compressible Euler equations of gas dynamics, showing that they are asymptotic-preserving (AP) in the low Mach number limit. The analysis is carried out for a general equation of state (EOS). We consider both a single asymptotic length scale and two length scales. We then show that, when coupling these time discretizations with a Discontinuous Galerkin (DG) space discretization with appropriate fluxes, a numerical method effective for a wide range of Mach numbers is obtained. A number of benchmarks for ideal gases and their non-trivial extension to non-ideal EOS validate the performed analysis.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113889"},"PeriodicalIF":3.8,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Change of measure for Bayesian field inversion with hierarchical hyperparameters sampling","authors":"Nadège Polette ,&nbsp;Olivier Le Maître ,&nbsp;Pierre Sochala ,&nbsp;Alexandrine Gesret","doi":"10.1016/j.jcp.2025.113888","DOIUrl":"10.1016/j.jcp.2025.113888","url":null,"abstract":"<div><div>This paper proposes an effective treatment of hyperparameters in the Bayesian inference of a scalar field from indirect observations. Obtaining the joint posterior distribution of the field and its hyperparameters is challenging. The infinite dimensionality of the field requires a finite parametrization that usually involves hyperparameters to reflect the limited prior knowledge. In the present work, we consider a Karhunen-Loève (KL) decomposition for the random field and hyperparameters to account for the lack of prior knowledge of its autocovariance function. The hyperparameters must be inferred. To efficiently sample jointly the KL coordinates of the field and the autocovariance hyperparameters, we introduce a change of measure to reformulate the joint posterior distribution into a hierarchical Bayesian form. The likelihood depends only on the field's coordinates in a fixed KL basis, with a prior conditioned on the hyperparameters. We exploit this structure to derive an efficient Markov Chain Monte Carlo (MCMC) sampling scheme based on an adapted Metropolis–Hasting algorithm. We rely on surrogate models (Polynomial Chaos expansions) of the forward model predictions to further accelerate the MCMC sampling. A first application to a transient diffusion problem shows that our method is consistent with other approaches based on a change of coordinates (Sraj et al., 2016, <span><span>[21]</span></span>). A second application to a seismic traveltime tomography highlights the importance of inferring the hyperparameters. A third application to a 2D anisotropic groundwater flow problem illustrates the method on a more complex geometry.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113888"},"PeriodicalIF":3.8,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations","authors":"Xu-Hui Zhou ,&nbsp;Jiequn Han ,&nbsp;Muhammad I. Zafar ,&nbsp;Eric M. Wolf ,&nbsp;Christopher R. Schrock ,&nbsp;Christopher J. Roy ,&nbsp;Heng Xiao","doi":"10.1016/j.jcp.2025.113871","DOIUrl":"10.1016/j.jcp.2025.113871","url":null,"abstract":"<div><div>Neural networks have recently emerged as powerful tools for accelerated solving of partial differential equations (PDEs) in both academic and industrial settings. However, their use as standalone surrogate models raises concerns about reliability, as solution accuracy heavily depends on data quality, volume, and training algorithms. This concern is particularly pronounced in tasks that prioritize computational precision and deterministic outcomes. In response, this study introduces “super-fidelity”, a method that employs neural networks for initial warm-starts, significantly speeding up the solution of steady-state PDEs without compromising on accuracy. Drawing from super-resolution in computer vision, super-fidelity maps solutions from low-fidelity computational models to high-fidelity ones using a vector-cloud neural network with equivariance (VCNN-e)—a neural operator that preserves physical symmetries and adapts to different spatial discretizations. We evaluated the proposed method across scenarios with varying degrees of nonlinearity, including (1) two-dimensional laminar flows around elliptical cylinders at low Reynolds numbers, exhibiting monotonic convergence, (2) two-dimensional turbulent flows over airfoils at high Reynolds numbers, characterized by oscillatory convergence, and (3) practical three-dimensional turbulent flows over a wing. The results demonstrate that our neural operator-based initialization can accelerate convergence by at least a factor of two while maintaining the same level of accuracy, outperforming traditional initialization methods using uniform fields or potential flows. The approach's robustness and scalability are confirmed across different linear equation solvers and multi-process computing configurations. Additional investigations highlight its reduced dependence on high quality of training data, and real time savings across multiple simulations, even when including the neural-network model preparation time. Our study presents a promising strategy for accelerated solving of steady-state PDEs using neural operators, ensuring high accuracy in applications where precision is of utmost importance.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113871"},"PeriodicalIF":3.8,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510540","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}