Journal of Computational Physics最新文献_第8页

Preventing mass loss in the standard level set method: New insights from variational analyses 防止标准水平集方法中的质量损失：变分分析的新见解

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-11 DOI: 10.1016/j.jcp.2024.113495

Kaustubh Khedkar , Amirreza Charchi Mamaghani , Pieter Ghysels , Neelesh A. Patankar , Amneet Pal Singh Bhalla

{"title":"Preventing mass loss in the standard level set method: New insights from variational analyses","authors":"Kaustubh Khedkar , Amirreza Charchi Mamaghani , Pieter Ghysels , Neelesh A. Patankar , Amneet Pal Singh Bhalla","doi":"10.1016/j.jcp.2024.113495","DOIUrl":"10.1016/j.jcp.2024.113495","url":null,"abstract":"<div><div>For decades, the computational multiphase flow community has grappled with mass loss in the level set method. Numerous solutions have been proposed, from fixing the reinitialization step to combining the level set method with other conservative schemes. However, our work reveals a more fundamental culprit: the smooth Heaviside and delta functions inherent to the standard formulation. Even if reinitialization is done exactly, i.e., the zero contour interface remains stationary, the use of smooth functions lead to violation of mass conservation. We propose a novel approach using variational analysis to incorporate a mass conservation constraint. This introduces a Lagrange multiplier that enforces overall mass balance. Notably, as the delta function sharpens, i.e., approaches the Dirac delta limit, the Lagrange multiplier approaches zero. However, the exact Lagrange multiplier method disrupts the signed distance property of the level set function. This motivates us to develop an approximate version of the Lagrange multiplier that preserves both overall mass and signed distance property of the level set function. Our framework even recovers existing mass-conserving level set methods, revealing some inconsistencies in prior analyses. We extend this approach to three-phase flows for fluid-structure interaction (FSI) simulations. We present variational equations in both immersed and non-immersed forms, demonstrating the convergence of the former formulation to the latter when the body delta function sharpens. Rigorous test problems confirm that the FSI dynamics produced by our simple, easy-to-implement immersed formulation with the approximate Lagrange multiplier method are accurate and match state-of-the-art solvers.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113495"},"PeriodicalIF":3.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441920","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

A DSMC-CFD coupling method using surrogate modelling for low-speed rarefied gas flows 低速稀薄气体流的代用建模 DSMC-CFD 耦合方法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-11 DOI: 10.1016/j.jcp.2024.113500

Giorgos Tatsios , Arun K. Chinnappan , Arshad Kamal , Nikos Vasileiadis , Stephanie Y. Docherty , Craig White , Livio Gibelli , Matthew K. Borg , James R. Kermode , Duncan A. Lockerby

{"title":"A DSMC-CFD coupling method using surrogate modelling for low-speed rarefied gas flows","authors":"Giorgos Tatsios , Arun K. Chinnappan , Arshad Kamal , Nikos Vasileiadis , Stephanie Y. Docherty , Craig White , Livio Gibelli , Matthew K. Borg , James R. Kermode , Duncan A. Lockerby","doi":"10.1016/j.jcp.2024.113500","DOIUrl":"10.1016/j.jcp.2024.113500","url":null,"abstract":"<div><div>A new Micro-Macro-Surrogate (MMS) hybrid method is presented that couples the Direct Simulation Monte Carlo (DSMC) method with Computational Fluid Dynamics (CFD) to simulate low-speed rarefied gas flows. The proposed MMS method incorporates surrogate modelling instead of direct coupling of DSMC data with the CFD, addressing the limitations CFD has in accurately modelling rarefied gas flows, the computational cost of DSMC for low-speed and multiscale flows, as well as the pitfalls of noise in conventional direct coupling approaches. The surrogate models, trained on the DSMC data using Bayesian inference, provide noise-free and accurate corrections to the CFD simulation enabling it to capture the non-continuum physics. The MMS hybrid approach is validated by simulating low-speed, steady-state, force-driven rarefied gas flows in a canonical 1D parallel-plate system, where corrections to the boundary conditions and stress tensor are considered and shows excellent agreement with DSMC benchmark results. A comparison with the typical domain decomposition DSMC-CFD hybrid method is also presented, to demonstrate the advantages of noise-avoidance in the proposed approach. The method also inherently captures the uncertainty arising from micro-model fluctuations, allowing for the quantification of noise-related uncertainty in the predictions. The proposed MMS method demonstrates the potential to enable multiscale simulations where CFD is inaccurate and DSMC is prohibitively expensive.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113500"},"PeriodicalIF":3.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442031","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

A performant energy-conserving particle reweighting method for Particle-in-Cell simulations 用于 "单元内粒子 "模拟的高性能能量守恒粒子再加权方法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-11 DOI: 10.1016/j.jcp.2024.113454

Jeremiah J. Boerner , Taylor Hall , Russell Hooper , Matthew T. Bettencourt , Matthew M. Hopkins , Anne M. Grillet , Jose L. Pacheco

引用次数: 0

Multiscale mixed methods with improved accuracy: The role of oversampling and smoothing 提高精度的多尺度混合方法：超采样和平滑的作用

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-10 DOI: 10.1016/j.jcp.2024.113490

Dilong Zhou , Rafael T. Guiraldello , Felipe Pereira

{"title":"Multiscale mixed methods with improved accuracy: The role of oversampling and smoothing","authors":"Dilong Zhou , Rafael T. Guiraldello , Felipe Pereira","doi":"10.1016/j.jcp.2024.113490","DOIUrl":"10.1016/j.jcp.2024.113490","url":null,"abstract":"<div><div>Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on multi-core supercomputers. Efficiency in obtaining numerical solutions is dictated by the choice of interface spaces that are selected: the smaller the dimension of these spaces, the better, in the sense that fewer multiscale basis functions need to be computed, and smaller interface linear systems need to be solved. Thus, in solving large computational problems, it is desirable to work with piecewise constant or linear polynomials for interface spaces. However, for these choices of interface spaces, it is well known that the flux accuracy is of the order of <span><math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>.</div><div>This study is dedicated to advancing an efficient and accurate multiscale mixed method aimed at addressing industry-relevant problems. A distinctive feature of our approach involves subdomains with overlapping regions, a departure from conventional methods. We take advantage of the overlapping decomposition to introduce a computationally highly efficient smoothing step designed to rectify small-scale errors inherent in the multiscale solution. The effectiveness of the proposed solver, which maintains a computational cost very close to its predecessors, is demonstrated through a series of numerical studies. Notably, for scenarios involving modestly sized overlapping regions and employing just a few smoothing steps, a substantial enhancement of two orders of magnitude in flux accuracy is achieved with the new approach.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113490"},"PeriodicalIF":3.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425963","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

Improved physics-informed neural networks for the reinterpreted discrete fracture model 用于重新解释离散断裂模型的改进型物理信息神经网络

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-10 DOI: 10.1016/j.jcp.2024.113491

Chao Wang , Hui Guo , Xia Yan , Zhang-Lei Shi , Yang Yang

{"title":"Improved physics-informed neural networks for the reinterpreted discrete fracture model","authors":"Chao Wang , Hui Guo , Xia Yan , Zhang-Lei Shi , Yang Yang","doi":"10.1016/j.jcp.2024.113491","DOIUrl":"10.1016/j.jcp.2024.113491","url":null,"abstract":"<div><div>This paper is the first attempt to apply improved-physics-informed neural networks (I-PINNs) to simulate fluid flow in fractured porous media based on the reinterpreted discrete fracture model (RDFM). The RDFM, first introduced by Xu and Yang, is a hybrid-dimensional model where Dirac-delta functions are used to characterize fractures and superposed with the permeability tensor. In this paper, we apply the physical information neural networks (PINNs) to RDFM. Different from the traditional PINNs where the PDE residual was used as the loss function, we adopt the finite element discretization of RDFM to build the loss function, avoiding the large gradient problem and difficulties in automatic differentiation. This new method is named as the improved PINNs (I-PINNs). Moreover, we combine the RDFM with incompressible miscible displacement in porous media. The bound-preserving technique of the I-PINNs is proposed and applied to the coupled system mentioned above, keeping the numerical concentration to be between 0 and 1. It is worth noting that one of the advantages of I-PINNs compared to PINNs is that it can better capture the pressure gradient at the fractures. Compared with traditional finite element methods for flow equations, I-PINNs do not request the inversion of the stiffness matrix. In addition, different from the traditional bound-preserving technique for contaminant transportation, I-PINNs preserve the physical bounds without taking a limited time step. Several numerical experiments are given to verify the feasibility and accuracy of the I-PINNs.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113491"},"PeriodicalIF":3.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425607","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

Adaptive hyperbolic-cross-space mapped Jacobi method on unbounded domains with applications to solving multidimensional spatiotemporal integrodifferential equations 无界域上的自适应双曲跨空间映射雅可比法及其在求解多维时空整微分方程中的应用

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-10 DOI: 10.1016/j.jcp.2024.113492

Yunhong Deng , Sihong Shao , Alex Mogilner , Mingtao Xia

引用次数: 0

The energy-diminishing weak Galerkin finite element method for the computation of ground state and excited states in Bose-Einstein condensates 计算玻色-爱因斯坦凝聚态基态和激发态的能量递减弱伽勒金有限元法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-10 DOI: 10.1016/j.jcp.2024.113497

Lin Yang , Xiang-Gui Li , Wei Yan , Ran Zhang

{"title":"The energy-diminishing weak Galerkin finite element method for the computation of ground state and excited states in Bose-Einstein condensates","authors":"Lin Yang , Xiang-Gui Li , Wei Yan , Ran Zhang","doi":"10.1016/j.jcp.2024.113497","DOIUrl":"10.1016/j.jcp.2024.113497","url":null,"abstract":"<div><div>In this paper, we employ the weak Galerkin (WG) finite element method and the imaginary time method to compute both the ground state and the excited states in Bose-Einstein condensate (BEC) which is governed by the Gross-Pitaevskii equation (GPE). First, we use the imaginary time method for GPE to get the nonlinear parabolic partial differential equation. Subsequently, we apply the WG method to spatially discretize the parabolic equation. This yields a semi-discrete scheme, in which an energy function is explicitly defined. For the case <span><math><mi>β</mi><mo>⩾</mo><mn>0</mn></math></span>, we demonstrate that the energy is diminishing with respect to time <em>t</em> at each time step. Applying the backward Euler scheme for temporal discretization yields a fully discrete scheme. For the case <span><math><mi>β</mi><mo>=</mo><mn>0</mn></math></span>, we provide a mathematical justification, establishing the convergence analysis for the numerical solution of the ground state. Moreover, based on the theory of solving eigenvalue problems using the WG method, we present the error estimates between the ground state and its numerical solution under the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norms. Numerical experiments are provided to illustrate the effectiveness of the proposed schemes. Moreover, the results indicate that our method also can compute the first excited state, achieving optimal convergence orders.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113497"},"PeriodicalIF":3.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433049","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

Error analysis of kernel/GP methods for nonlinear and parametric PDEs 非线性和参数 PDE 的核/GP 方法的误差分析

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-10 DOI: 10.1016/j.jcp.2024.113488

Pau Batlle , Yifan Chen , Bamdad Hosseini , Houman Owhadi , Andrew M. Stuart

{"title":"Error analysis of kernel/GP methods for nonlinear and parametric PDEs","authors":"Pau Batlle , Yifan Chen , Bamdad Hosseini , Houman Owhadi , Andrew M. Stuart","doi":"10.1016/j.jcp.2024.113488","DOIUrl":"10.1016/j.jcp.2024.113488","url":null,"abstract":"<div><div>We introduce a priori Sobolev-space error estimates for the solution of arbitrary nonlinear, and possibly parametric, PDEs that are defined in the strong sense, using Gaussian process and kernel based methods. The primary assumptions are: (1) a continuous embedding of the reproducing kernel Hilbert space of the kernel into a Sobolev space of sufficient regularity; and (2) the stability of the differential operator and the solution map of the PDE between corresponding Sobolev spaces. The proof is articulated around Sobolev norm error estimates for kernel interpolants and relies on the minimizing norm property of the solution. The error estimates demonstrate dimension-benign convergence rates if the solution space of the PDE is smooth enough. We illustrate these points with applications to high-dimensional nonlinear elliptic PDEs and parametric PDEs. Although some recent machine learning methods have been presented as breaking the curse of dimensionality in solving high-dimensional PDEs, our analysis suggests a more nuanced picture: there is a trade-off between the regularity of the solution and the presence of the curse of dimensionality. Therefore, our results are in line with the understanding that the curse is absent when the solution is regular enough.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113488"},"PeriodicalIF":3.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535525","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

High-order schemes of exponential time differencing for stiff systems with nondiagonal linear part 具有非对角线性部分的刚性系统的指数时差高阶方案

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-10 DOI: 10.1016/j.jcp.2024.113493

Evelina V. Permyakova , Denis S. Goldobin

{"title":"High-order schemes of exponential time differencing for stiff systems with nondiagonal linear part","authors":"Evelina V. Permyakova , Denis S. Goldobin","doi":"10.1016/j.jcp.2024.113493","DOIUrl":"10.1016/j.jcp.2024.113493","url":null,"abstract":"<div><div>Exponential time differencing methods are a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models often possess fast oscillating or decaying modes—in other words, are stiff systems. Practical implementation of these methods for the systems with nondiagonal linear part of equations is exacerbated by infeasibility of an analytical calculation of the exponential of a nondiagonal linear operator; in this case, the coefficients of the exponential time differencing scheme cannot be calculated analytically. We suggest an approach, where these coefficients are numerically calculated with auxiliary problems. We rewrite the high-order Runge–Kutta type schemes in terms of the solutions to these auxiliary problems and practically examine the accuracy and computational performance of these methods for a heterogeneous Cahn–Hilliard equation, a sixth-order spatial derivative equation governing pattern formation in the presence of an additional conservation law, and a Fokker–Planck equation governing macroscopic dynamics of a network of neurons.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113493"},"PeriodicalIF":3.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425885","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

The method of fundamental solutions for multi-particle Stokes flows: Application to a ring-like array of spheres 多粒子斯托克斯流的基本解法：对环状球阵列的应用

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-10-10 DOI: 10.1016/j.jcp.2024.113487

Josiah J.P. Jordan, Duncan A. Lockerby

{"title":"The method of fundamental solutions for multi-particle Stokes flows: Application to a ring-like array of spheres","authors":"Josiah J.P. Jordan, Duncan A. Lockerby","doi":"10.1016/j.jcp.2024.113487","DOIUrl":"10.1016/j.jcp.2024.113487","url":null,"abstract":"<div><div>A method is presented for calculating Stokes flow around multiple particles of arbitrary shape. It uses the Method of Fundamental Solutions (MFS) applied to single particles, combined with an iterative scheme to resolve the many particle-particle hydrodynamic interactions; an approach that is reminiscent of the Method of Reflections. The attractive features of the proposed method are inherited from the MFS — simplicity and accuracy — while providing orders of magnitude computational speed-up for large particle systems. The method is verified through a series of test cases, including those involving strong lubrication forces and non-spherical particles. Unlike applications of the Method of Reflections reported in the literature, the iterative scheme we propose (a block Gauss-Seidel approach to solving a particle-particle interaction matrix) converges for all the cases we consider, for both resistance and mobility problems. The scheme is applied to the study of Stokes flow around ring-like arrays of spheres. We show that the relationship between globally applied velocity or force to the response of individual spheres can be described by just 5 coefficients (or 9 in total) for any given configuration. The results indicate that for 7–10 spheres in sedimentation, there exists a certain spacing that produces steady-state translation of the ring, independent of its orientation. For large numbers of spheres, slender-body theory can be applied to the problem, providing remarkably close agreement to the numerical results over a wide range of parameters.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113487"},"PeriodicalIF":3.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433045","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