Journal of Computational Physics最新文献

Taylor series error correction network for super-resolution of discretized partial differential equation solutions 用于离散化偏微分方程解超分辨率的泰勒级数纠错网络

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-15 DOI: 10.1016/j.jcp.2024.113569

Wenzhuo Xu, Christopher McComb, Noelia Grande Gutiérrez

{"title":"Taylor series error correction network for super-resolution of discretized partial differential equation solutions","authors":"Wenzhuo Xu, Christopher McComb, Noelia Grande Gutiérrez","doi":"10.1016/j.jcp.2024.113569","DOIUrl":"10.1016/j.jcp.2024.113569","url":null,"abstract":"<div><div>High-fidelity engineering simulations can impose an enormous computational burden, hindering their application in design processes or other scenarios where time or computational resources can be limited. An effective up-sampling method for generating high-resolution data can help reduce the computational resources and time required for these simulations. However, conventional up-sampling methods encounter challenges when estimating results based on low-resolution meshes due to the often non-linear behavior of discretization error induced by the coarse mesh. In this study, we present the Taylor Expansion Error Correction Network (TEECNet), a neural network designed to efficiently super-resolve partial differential equations (PDEs) solutions via graph representations. We use a neural network to learn high-dimensional non-linear mappings between low- and high-fidelity solution spaces to approximate the effects of discretization error. The learned mapping is then applied to the low-fidelity solution to obtain an error correction model. Building upon the notion that discretization error can be expressed as a Taylor series expansion based on the mesh size, we directly encode approximations of the numerical error in the network design. This novel approach is capable of correcting point-wise evaluations and emulating physical laws in infinite-dimensional solution spaces. Additionally, results from computational experiments verify that the proposed model exhibits the ability to generalize across diverse physics problems, including heat transfer, Burgers' equation, and cylinder wake flow, achieving over 96% accuracy by mean squared error and a 42.76% reduction in computation cost compared to popular operator regression methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113569"},"PeriodicalIF":3.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653186","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}

引用次数: 0

Registration-based nonlinear model reduction of parametrized aerodynamics problems with applications to transonic Euler and RANS flows 基于注册的参数化空气动力学问题非线性模型缩减，应用于跨音速欧拉流和 RANS 流

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-15 DOI: 10.1016/j.jcp.2024.113576

Alireza H. Razavi, Masayuki Yano

{"title":"Registration-based nonlinear model reduction of parametrized aerodynamics problems with applications to transonic Euler and RANS flows","authors":"Alireza H. Razavi, Masayuki Yano","doi":"10.1016/j.jcp.2024.113576","DOIUrl":"10.1016/j.jcp.2024.113576","url":null,"abstract":"<div><div>We develop a registration-based nonlinear model-order reduction (MOR) method for partial differential equations (PDEs) with applications to transonic Euler and Reynolds-averaged Navier–Stokes (RANS) equations in aerodynamics. These PDEs exhibit discontinuous features, namely shocks, whose location depends on problem configuration parameters, and the associated parametric solution manifold exhibits a slowly decaying Kolmogorov <em>N</em>-width. As a result, conventional linear MOR methods, which use linear reduced approximation spaces, do not yield accurate low-dimensional approximations. We present a registration-based nonlinear MOR method to overcome this challenge. Our formulation builds on the following key ingredients: (i) a geometrically transformable parametrized PDE discretization; (ii) localized spline-based parametrized transformations which warp the domain to align discontinuities; (iii) an efficient dilation-based shock sensor and metric to compute optimal transformation parameters; (iv) hyperreduction and online-efficient output-based error estimates; and (v) simultaneous transformation and adaptive finite element training. Compared to existing methods in the literature, our formulation is efficiently scalable to larger problems and is equipped with error estimates and hyperreduction. We demonstrate the effectiveness of the method on two-dimensional inviscid and turbulent flows modeled by the Euler and RANS equations, respectively.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113576"},"PeriodicalIF":3.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653061","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}

引用次数: 0

Local energy-preserving scalar auxiliary variable approaches for general multi-symplectic Hamiltonian PDEs 一般多交映哈密顿 PDE 的局部能量守恒标量辅助变量方法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-14 DOI: 10.1016/j.jcp.2024.113573

Jiaxiang Cai , Yushun Wang

引用次数: 0

ARMS: Adding and removing markers on splines for high-order general interface tracking under the MARS framework ARMS：在 MARS 框架下为高阶一般界面跟踪添加和删除样条上的标记

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-14 DOI: 10.1016/j.jcp.2024.113574

Difei Hu , Kaiyi Liang , Linjie Ying , Sen Li , Qinghai Zhang

{"title":"ARMS: Adding and removing markers on splines for high-order general interface tracking under the MARS framework","authors":"Difei Hu , Kaiyi Liang , Linjie Ying , Sen Li , Qinghai Zhang","doi":"10.1016/j.jcp.2024.113574","DOIUrl":"10.1016/j.jcp.2024.113574","url":null,"abstract":"<div><div>Based on the MARS framework for interface tracking (IT) (Zhang and Fogelson (2016) <span><span>[33]</span></span>) (Zhang and Li (2020) <span><span>[35]</span></span>), we propose ARMS (adding and removing markers on splines as a strategy for regularizing distances between adjacent markers in simulating moving boundary problems. In ARMS, we represent the interface by cubic/quintic splines and add/remove interface markers at each time step to maintain a roughly uniform distribution of chordal lengths. To demonstrate the utility of ARMS, we apply it to two-dimensional mean curvature flows to develop ARMS-MCF2D, where spatial derivatives are approximated by finite difference formulas and the resulting nonlinear system of ordinary differential equations is solved by explicit, semi-implicit, and implicit Runge–Kutta methods. As such, the semi-implicit and implicit ARMS-MCF2D methods are unconditionally stable. Error analysis indicates that the order of accuracy of ARMS-MCF2D can be 2, 4, or 6. Results of numerical experiments confirm the analysis, show the effectiveness of ARMS in maintaining the regularity of interface markers, and demonstrate the superior accuracy of ARMS-MCF2D over other existing methods. A one-phase Stefan problem is also simulated by coupling ARMS to a finite difference method, exhibiting its potential utility to general IT in moving boundary problems. The generality and flexibility of ARMS partially lie in the fact that, by specifying a discrete time integrator for her own moving boundary problem, an application scientist immediately obtains a MARS method for the problem without worrying about curve fitting and marker distributions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113574"},"PeriodicalIF":3.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653059","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}

引用次数: 0

A hybrid a posteriori MOOD limited lattice Boltzmann method to solve compressible fluid flows – LBMOOD 解决可压缩流体流动的混合后验 MOOD 有限晶格玻尔兹曼法 - LBMOOD

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-13 DOI: 10.1016/j.jcp.2024.113570

Ksenia Kozhanova , Song Zhao , Raphaël Loubère , Pierre Boivin

引用次数: 0

On the accuracy of numerical methods for the discretization of anisotropic elliptic problems 关于各向异性椭圆问题离散化数值方法的精度

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-12 DOI: 10.1016/j.jcp.2024.113568

Chang Yang , Fabrice Deluzet , Jacek Narski

引用次数: 0

Ray decomposition radiation transport for high performance computing 用于高性能计算的射线分解辐射传输

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-12 DOI: 10.1016/j.jcp.2024.113567

Owen Mylotte, Matthew T. McGurn, Kenneth Budzinski, Paul E. DesJardin

引用次数: 0

Stability and robustness of time-discretization schemes for the Allen-Cahn equation via bifurcation and perturbation analysis 通过分岔和扰动分析看艾伦-卡恩方程时间离散化方案的稳定性和稳健性

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-08 DOI: 10.1016/j.jcp.2024.113565

Wenrui Hao , Sun Lee , Xiaofeng Xu , Zhiliang Xu

{"title":"Stability and robustness of time-discretization schemes for the Allen-Cahn equation via bifurcation and perturbation analysis","authors":"Wenrui Hao , Sun Lee , Xiaofeng Xu , Zhiliang Xu","doi":"10.1016/j.jcp.2024.113565","DOIUrl":"10.1016/j.jcp.2024.113565","url":null,"abstract":"<div><div>The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently utilized time-discretization numerical schemes for solving the Allen-Cahn equation, with focuses on the Backward Euler, Crank-Nicolson (CN), convex splitting of modified CN, and Diagonally Implicit Runge-Kutta (DIRK) methods. Our stability analysis reveals that the Convex Splitting of the Modified CN scheme exhibits unconditional stability, allowing greater flexibility in time step size selection, while the other schemes are conditionally stable. Additionally, our robustness analysis highlights that the Backward Euler method converges to correct physical solutions regardless of initial conditions. In contrast, all other methods studied in this work show sensitivity to initial conditions and may converge to incorrect physical solutions if the initial conditions are not carefully chosen. This study introduces a comprehensive approach to assessing stability and robustness in numerical methods for solving the Allen-Cahn equation, providing a new perspective for evaluating numerical techniques for general nonlinear differential equations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113565"},"PeriodicalIF":3.8,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653179","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}

引用次数: 0

Gradient-boosted spatiotemporal neural network for simulating underground hydrogen storage in aquifers 用于模拟含水层地下储氢的梯度提升时空神经网络

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-08 DOI: 10.1016/j.jcp.2024.113557

Jian Wang , Zongwen Hu , Xia Yan , Jun Yao , Hai Sun , Yongfei Yang , Lei Zhang , Junjie Zhong

{"title":"Gradient-boosted spatiotemporal neural network for simulating underground hydrogen storage in aquifers","authors":"Jian Wang , Zongwen Hu , Xia Yan , Jun Yao , Hai Sun , Yongfei Yang , Lei Zhang , Junjie Zhong","doi":"10.1016/j.jcp.2024.113557","DOIUrl":"10.1016/j.jcp.2024.113557","url":null,"abstract":"<div><div>Underground hydrogen storage (UHS) in aquifers has emerged as a viable solution to address the seasonal mismatch between supply and demand in renewable energy. Numerical simulation of the UHS serves as a crucial foundation for optimizing storage operations and conducting system risk assessments. However, numerical simulation methods employed for these purposes often demand substantial data, making data collection challenging and computationally expensive, especially in scenarios involving the coupling of multiple physical fields. Deep learning serves as an effective tool in resolving this challenge. Here, we proposed a spatiotemporal neural network architecture with gradient enhancement, denoted as gradient-boosted spatiotemporal neural network (GSTNN) and its variant GSTNN-s. The GSTNN combines a convolutional neural network (CNN), a long short-term memory network (LSTM), and an autoencoder architecture. To incorporate physical constraints into the network, the spatiotemporal gradient operators from the gas-water seepage and gas convection-diffusion equations are introduced as regularization terms, imposing physics-informed constraints on the training process in both temporal and spatial dimensions. In predicting the multiphase flow of UHS in both homogeneous and heterogeneous formations, GSTNN outperforms CNN and CNN-LSTM in terms of the accuracy of pressure, saturation and H<sub>2</sub> concentration fields. In terms of predicting UHS in formations with different permeabilities and porosities, GSTNN-s demonstrates improved performance as well. The proposed GSTNN architecture is promising in improving the efficiency of UHS numerical simulation, and has great potential to be applied for optimizing UHS operations in the future.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113557"},"PeriodicalIF":3.8,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653181","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}

引用次数: 0

Stiefel manifold interpolation for non-intrusive model reduction of parameterized fluid flow problems 用于参数化流体流动问题非侵入式模型缩减的 Stiefel 流形插值法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-11-07 DOI: 10.1016/j.jcp.2024.113564

Achraf El Omari , Mohamed El Khlifi , Laurent Cordier

{"title":"Stiefel manifold interpolation for non-intrusive model reduction of parameterized fluid flow problems","authors":"Achraf El Omari , Mohamed El Khlifi , Laurent Cordier","doi":"10.1016/j.jcp.2024.113564","DOIUrl":"10.1016/j.jcp.2024.113564","url":null,"abstract":"<div><div>Many engineering problems are parameterized. In order to minimize the computational cost necessary to evaluate a new operating point, the interpolation of singular matrices representing the data seems natural. Unfortunately, interpolating such data by conventional methods usually leads to unphysical solutions, as the data live on manifolds and not vector spaces. An alternative is to perform the interpolation in the tangent space to the Grassmann manifold to obtain interpolated spatial modes. Temporal modes are afterwards determined via the Galerkin projection of the high-fidelity model onto the interpolated spatial basis. This method, which is known for some fifteen years, is intrusive. Recently, Oulghelou and Allery (JCP, 2021) have proposed a non-intrusive approach (equation-free), but requiring the resolution of two low-dimensional optimization problems after interpolation. In this paper, a non-intrusive alternative based on Interpolation on the Tangent Space of the Stiefel Manifold (ITSSM) is presented. This approach has the advantage of not requiring a calibration phase after interpolation. To assess the method, we compare our results with those obtained using global POD on the one hand, and two methods based on Grassmann interpolation on the other. These comparisons are performed for two classical configurations encountered in fluid dynamics. The first corresponds to the one-dimensional non-linear Burgers' equation. The second example is the two-dimensional cylinder wake flow. We show that the proposed strategy can accurately reconstruct the physical quantities associated with a new operating point. Moreover, the estimation is fast enough to allow real-time computation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113564"},"PeriodicalIF":3.8,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660003","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}

引用次数: 0