Journal of Computational Physics最新文献

{"title":"Reduced basis methods for parametric steady-state radiative transfer equation","authors":"Kimberly Matsuda ,&nbsp;Yanlai Chen ,&nbsp;Yingda Cheng ,&nbsp;Fengyan Li","doi":"10.1016/j.jcp.2025.114597","DOIUrl":"10.1016/j.jcp.2025.114597","url":null,"abstract":"<div><div>The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium, and it arises in many applications. Deterministic methods can produce accurate solutions without any statistical noise, yet often at a price of expensive computational costs originating from the intrinsic high dimensionality of the model. This is more prominent in multi-query tasks, e.g., inverse problems and optimal design, when the RTE needs to be solved repeatedly. This motivates the developments of dimensionality and model order reduction techniques for such transport models.</div><div>With this work, we present the first systematic investigation of projection-based reduced order models (ROMs) following the reduced basis method (RBM) framework to simulate the parametric steady-state RTE with isotropic scattering and one energy group. The use of RBM compared to standard proper orthogonal decomposition (POD) is well motivated, especially considering that a large number of degrees of freedom is needed by full order models to solve high dimensional transport models like RTE. Four ROMs are designed, with each defining a nested family of reduced surrogate solvers of different resolution/fidelity. They are based on either a Galerkin or least-squares Petrov-Galerkin projection and utilize either an <em>L</em>₁ or residual-based importance/error indicator. Two of the proposed ROMs are certified in the setting when the absorption cross section is positively bounded below uniformly. One technical focus and contribution lie in the proposed implementation strategies under the affine assumption of the parameter dependence of the model. These well-crafted broadly applicable strategies not only ensure the efficiency and accuracy of the offline training stage and the online prediction of reduced surrogate solvers, they also take into account the conditioning of the reduced systems as well as the stagnation-free residual evaluation for numerical robustness. Computational complexities are derived for both the offline training and online prediction stages of the proposed model order reduction strategies, and they are demonstrated numerically along with the accuracy and robustness of the reduced surrogate solvers. Numerically we observe four to six orders of magnitude speedup of our ROMs compared to full order models for some 2D2v examples.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114597"},"PeriodicalIF":3.8,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837829","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":"Effects of lower floating-point precision on scale-resolving numerical simulations of turbulence","authors":"Martin Karp ,&nbsp;Ronith Stanly ,&nbsp;Timofey Mukha ,&nbsp;Luca Galimberti ,&nbsp;Siavash Toosi ,&nbsp;Hang Song ,&nbsp;Lisandro Dalcin ,&nbsp;Saleh Rezaeiravesh ,&nbsp;Niclas Jansson ,&nbsp;Stefano Markidis ,&nbsp;Matteo Parsani ,&nbsp;Sanjeeb Bose ,&nbsp;Sanjiva Lele ,&nbsp;Philipp Schlatter","doi":"10.1016/j.jcp.2025.114600","DOIUrl":"10.1016/j.jcp.2025.114600","url":null,"abstract":"<div><div>Modern computing clusters offer specialized hardware for reduced-precision arithmetic, which can significantly speed up the time to solution. This is possible due to a decrease in data movement, as well as the ability to perform arithmetic operations at a faster rate. However, for high-fidelity simulations of turbulence, such as direct and large-eddy simulation, the impact of reduced precision on the computed solution and the resulting uncertainty across flow solvers and different flow cases has not been explored in detail, and limits the optimal utilization of new high-performance computing systems. In this work, the effect of reduced precision is studied using four diverse computational fluid dynamics (CFD) solvers (two incompressible, Neko and Simson, and two compressible, PadeLibs and SSDC) using four test cases: turbulent channel flow at <span><math><mrow><mi>R</mi><msub><mi>e</mi><mi>τ</mi></msub><mo>=</mo><mn>550</mn></mrow></math></span> and higher, forced transition in a channel, flow over a cylinder at <span><math><mrow><mi>R</mi><msub><mi>e</mi><mi>D</mi></msub><mo>=</mo><mn>3900</mn></mrow></math></span>, and compressible flow over a wing section at <span><math><mrow><mi>R</mi><msub><mi>e</mi><mi>c</mi></msub><mo>=</mo><mn>50000</mn></mrow></math></span>. We observe that the flow physics are remarkably robust with respect to reductions in lower floating-point precision, and that often other forms of uncertainty, due to, for example, time averaging, often have a much larger impact on the computed result. Our results indicate that different terms in the Navier–Stokes equations can be computed to a lower floating-point accuracy without affecting the results. In particular, standard IEEE single precision can be used effectively for the entirety of the simulation, showing no significant discrepancies from double-precision results across the solvers and cases considered. Potential pitfalls are also discussed.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114600"},"PeriodicalIF":3.8,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838741","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":"Fully quantum lattice gas automata building blocks for computational basis state encodings","authors":"Călin A. Georgescu,&nbsp;Merel A. Schalkers,&nbsp;Matthias Möller","doi":"10.1016/j.jcp.2025.114595","DOIUrl":"10.1016/j.jcp.2025.114595","url":null,"abstract":"<div><div>Lattice Gas Automata (LGA) is a classical method for simulating physical phenomena, including Computational Fluid Dynamics (CFD). Quantum LGA (QLGA) is the family of methods that implement LGA schemes on quantum computers. In recent years, QLGA has garnered attention from researchers thanks to its potential of efficiently modeling CFD processes by either reducing memory requirements or providing simultaneous representations of exponentially many LGA states. In this work, we introduce novel building blocks for QLGA algorithms that rely on computational basis state encodings. We address every step of the algorithm, from initial conditions to measurement, and provide detailed complexity analyses that account for all discretization choices of the system under simulation. We introduce multiple ways of instantiating initial conditions, efficient boundary condition implementations for novel geometrical patterns, a novel collision operator that models less restricted interactions than previous implementations, and quantum circuits that extract quantities of interest out of the quantum state. For each building block, we provide intuitive examples and open-source implementations of the underlying quantum circuits.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114595"},"PeriodicalIF":3.8,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Physics-informed machine learning for wetting hydrodynamics","authors":"Andreas D. Demou ,&nbsp;Panayiotis-Yiannis Vrionis ,&nbsp;Nikos Savva","doi":"10.1016/j.jcp.2025.114596","DOIUrl":"10.1016/j.jcp.2025.114596","url":null,"abstract":"<div><div>This study presents a data-driven approach for modeling wetting hydrodynamics phenomena in the form of droplet transport on chemically heterogeneous surfaces, utilizing prior physical knowledge. The training datasets are generated using direct numerical simulations of the two-phase Stokes equations, applicable in the low Reynolds number limit. The resulting data-driven models are based on the Fourier neural operator and are trained to correct the time derivative of the contact line as predicted by a low-order asymptotic approximation, an approach that was proven to be accurate and generalizable in earlier studies that focused on wetting hydrodynamics in the long-wave regime. More specifically, two data-driven models are trained to augment the low-order contact line velocity prediction: (i) a model focusing on correcting the purely translational velocity component of the droplet, and (ii) a model focusing on the higher-order corrections to the contact line velocity. The corrected contact line velocity is then used to advance the solution in time, using standard time-integration schemes. The resulting physics-informed machine learning workflow is proven to accurately capture the contact line dynamics on a range of different substrate heterogeneity profiles and can provide a reliable and efficient alternative to costly direct numerical simulations in optimization tasks, where a large number of simulations are needed.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114596"},"PeriodicalIF":3.8,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837823","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 adaptive stabilized finite element method for coupled nonlinear reaction-diffusion systems","authors":"Chong Liu ,&nbsp;Juan F. Giraldo ,&nbsp;Victor M. Calo ,&nbsp;Klaus Regenauer-Lieb ,&nbsp;Manman Hu","doi":"10.1016/j.jcp.2025.114598","DOIUrl":"10.1016/j.jcp.2025.114598","url":null,"abstract":"<div><div>Reaction-diffusion systems are pivotal in developing spatiotemporal patterns across various scientific and engineering disciplines, including physical and chemical processes, biology, electrochemical systems, and materials science. This study presents an adaptively stabilized finite element method (ASFEM) that simulates the formation of these patterns for reaction-diffusion systems with and without cross-diffusion. The models capture complex natural patterns such as spots, stripes, spirals, and traveling waves. The proposed approach employs a residual minimization process within a stable discontinuous Galerkin (dG) dual norm, resulting in discretely stable saddle-point problems and robust error estimates that guide mesh adaptivity. We demonstrate the method’s accuracy and efficiency across several scenarios, with solution quality and performance comparable to analytical solutions and classical continuous Galerkin (cG) formulations. We model several coupled reaction-diffusion systems using the advanced adaptive technique; these models include dynamic pattern evolution in the activator-inhibitor, Gray-Scott, and Brusselator models, as well as wave propagation and spiral formation in the FitzHugh-Nagumo model. The results indicate the effectiveness of the refinement technique in capturing highly localized solution characteristics. Our approach extends to large, multidimensional problems in scientific research and industrial applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114598"},"PeriodicalIF":3.8,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837827","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":"SPH modelling of water flow inside a fixed and undeformable porous medium using a Riemann based formulation","authors":"Coline De Sousa ,&nbsp;Marin Lallemand ,&nbsp;Guillaume Oger ,&nbsp;Julien Michel ,&nbsp;David Le Touzé ,&nbsp;Damien Violeau","doi":"10.1016/j.jcp.2025.114588","DOIUrl":"10.1016/j.jcp.2025.114588","url":null,"abstract":"<div><div>A weakly-compressible Smoothed Particle Hydrodynamics (SPH) model for the simulation of water seepage in a fixed and undeformable porous matrix is proposed in this paper. Within this model, the macroscopic governing equations of mass and momentum are expressed using an averaging process on an elementary volume of porous medium. A first set of particles is used for modelling the fluid, while a second one is employed for the porous structure to compute the volume fraction involved in the volume-averaged equations. The stabilization of the fluid model, based on a Riemann solver, is free of any diffusion parameter and results in regular and accurate pressure fields. Moreover, a Boundary Integral Method is chosen in this work to handle wall boundary conditions, with use of the so-called Español and Revenga laplacian operator. To the authors’ knowledge, both this stabilization and wall treatment technique have never been applied yet to this field of application. The validation of the present model on three test-cases demonstrates its strong reliability, showing good agreement with numerical and experimental results from the literature.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"549 ","pages":"Article 114588"},"PeriodicalIF":3.8,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838743","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":"Topological derivative multiscale approach for the design of broadband epsilon-near-zero metamaterials","authors":"A.A. Novotny ,&nbsp;F.A. Pinheiro ,&nbsp;P.J. Blanco","doi":"10.1016/j.jcp.2025.114594","DOIUrl":"10.1016/j.jcp.2025.114594","url":null,"abstract":"<div><div>We put forward a novel application of the topological derivative method, in the context of multiscale electromagnetic material modeling, to the design of epsilon-near-zero (ENZ) metamaterials. Unlike conventional homogenization techniques, the proposed approach is valid for a broad frequency range and benefits from a well-defined variational structure. Leveraging this structure, we derive the sensitivity of the effective macroscopic electric permittivity tensor to microscale topological changes. By predicting unique ENZ plasmonic composites at a desired broad range of visible and near-infrared wavelengths, we demonstrate that the topological derivative approach allows for a systematic design of optimized ENZ metamaterials with nontrivial, unprecedented geometries responsible for functionalities that cannot be achieved with traditional metamaterial synthesis techniques.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114594"},"PeriodicalIF":3.8,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837828","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":"Parameterized analytical solution of seepage equation for reservoir simulation using physics-informed kolmogorov-arnold network without labels","authors":"Qian Wang ,&nbsp;Wenshu Zha ,&nbsp;Daolun Li ,&nbsp;Xiang Li ,&nbsp;Luhang Shen ,&nbsp;Zhengzheng Shi","doi":"10.1016/j.jcp.2025.114599","DOIUrl":"10.1016/j.jcp.2025.114599","url":null,"abstract":"<div><div>Partial differential equations (PDEs) play a crucial role in the description of physical phenomena; however, traditional numerical methods face significant challenges regarding computational complexity and high-dimensional problems. Although Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving PDEs, they face certain limitations in terms of generalization and computational efficiency, particularly for complex problems such as the seepage equation with source-sink terms. We propose an innovative method for solving the seepage equation with source-sink terms efficiently and accurately, without labels, without meshing, using asymptotic networks and Physically Informed Kolmogorov-Arnold Network (AS-PIKAN), and express its parameterized analytical form with parameters. This model combines asymptotic and correction networks. The asymptotic network captures the asymptotic behavior of the equation and offers initial approximations, whereas the correction network leverages the interpretability of KAN for refinement. Ultimately, we derive a mathematical expression for the parameterized analytical solution of the seepage equation. Experimental results show that after obtaining the parameterized analytical solution, its solving speed is about 4.3 times faster than traditional numerical methods, while maintaining a solution accuracy within the range of 10^–4 to 10^–2.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114599"},"PeriodicalIF":3.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837818","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":"Second order accurate discretization of the material point method on periodic domains","authors":"Song Bai ,&nbsp;Michael (Fox) Liu ,&nbsp;Craig Schroeder","doi":"10.1016/j.jcp.2025.114589","DOIUrl":"10.1016/j.jcp.2025.114589","url":null,"abstract":"<div><div>In this paper, we propose a second order accurate discretization of the Material Point Method (MPM) based on an explicit midpoint scheme. This discretization uses quadratic PolyPIC to transfer velocities between particles and the grid, reducing particle noise and allowing transfers to support irregular boundaries. We propose corrections for the velocity derivatives stored on particles by PolyPIC to account for the effects of particle movement. The method of manufactured solutions provides a powerful and robust strategy for evaluating the accuracy of numerical methods, especially ones for which general analytic solutions are lacking. The method of manufactured solutions has always been difficult to apply to MPM due to the need for both an analytic velocity and an analytic deformation gradient, which must be consistent. We present a general strategy for constructing and implementing manufactured solutions for MPM formulated in terms of the inverse of the deformation map. This strategy decouples the analytic solution from the constitutive model, making it feasible to test MPM implementations over a wider range of analytic solutions and constitutive models. We demonstrate that the scheme is second order accurate under refinement in both the <em>L</em>₂ and <em>L</em>_∞ norms for both the velocity and deformation gradient.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114589"},"PeriodicalIF":3.8,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798662","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":"Generalized synthetic inflow generation method for divergence-free inhomogeneous turbulence","authors":"Anjia Ying ,&nbsp;Zhigang Li ,&nbsp;Lin Fu","doi":"10.1016/j.jcp.2025.114593","DOIUrl":"10.1016/j.jcp.2025.114593","url":null,"abstract":"<div><div>A generalized synthetic inflow (GSI) turbulence generation method is proposed in this study for divergence-free inlet boundary conditions where the flow properties can be inhomogeneous in space. The GSI describes the turbulence with eigenmodes of spatiotemporal covariance of velocity fluctuations in the inhomogeneous directions to guarantee the orthogonality of the synthesizing bases, which is crucial to the preservation of the target spectral properties. To meet the solenoidal condition, the divergence is first minimized in the sense of integrated variance at the inlet boundary while keeping the spectral properties unchanged by optimizing the phases of the eigenmodes. Then, the divergence is eliminated by minimally adjusting the velocity by solving a quadratic programming problem. In cases where the detailed spatiotemporal covariance is not available for the GSI framework, the targeted Reynolds-stress and length-scale (TRL) model is proposed, which reconstructs the covariance of the flow field with targeted Reynolds stress and length scales. The GSI framework is then validated in both idealized homogeneous turbulence with various settings of prescribed statistics and the turbulent boundary layer (TBL) with strong inhomogeneity and anisotropy. Compared to existing synthetic methods, GSI demonstrates robust performance in reproducing the targeted turbulence properties at the inlet on the premise of the divergence-free condition and preserving downstream turbulence spectral properties in large-eddy simulation (LES). Further, the GSI is validated in direct numerical simulation (DNS) of TBL. With either actual or TRL-modeled covariance, the GSI requires a recovery length of around 10 times the boundary-layer thickness at the inlet plane, which is less than half of that achieved with the tested recycling-rescaling-based method. This underscores the potential of the GSI framework for fundamental research and engineering applications in wall-bounded flows.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"548 ","pages":"Article 114593"},"PeriodicalIF":3.8,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798653","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}