扭曲网格上三维对流扩散方程的单元中心正保全有限体积方案

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Gang Peng
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引用次数: 0

摘要

本文旨在构建适用于任意多面体网格的三维对流扩散方程的保正有限体积方案。扩散通量采用经典的非线性两点通量近似法离散化。为确保完全离散方案具有正保全特性,提出了一种改进的对流通量离散方法。此外,还从对流通量离散化的线性重构中推导出了一种新的保正顶点插值方法。此外,Picard 迭代法在求解非线性系统时可能收敛较慢。因此,采用了 Picard 迭代法的 Anderson 加速法来求解非线性系统。新方案适用于任意多面体网格,并具有二阶精度。数值实验结果也证实了离散化方案的保正性。本文针对三维对流扩散方程提出了一种新的保正有限体积方案。2.构建了新的对流通量离散化方案。3.给出了一种新的二阶插值算法,以消除通量表达式中的辅助未知量。4.采用改进的安德森加速法加速 Picard 迭代的收敛。5.该方案能以二阶精度求解扭曲网格上的对流扩散方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The cell-centered positivity-preserving finite volume scheme for 3D convection–diffusion equation on distorted meshes

Purpose

This paper aims to construct positivity-preserving finite volume schemes for the three-dimensional convection–diffusion equation that are applicable to arbitrary polyhedral grids.

Design/methodology/approach

The cell vertices are used to define the auxiliary unknowns, and the primary unknowns are defined at cell centers. The diffusion flux is discretized by the classical nonlinear two-point flux approximation. To ensure the fully discrete scheme has positivity-preserving property, an improved discretization method for the convection flux was presented. Besides, a new positivity-preserving vertex interpolation method is derived from the linear reconstruction in the discretization of convection flux. Moreover, the Picard iteration method may have slow convergence in solving the nonlinear system. Thus, the Anderson acceleration of Picard iteration method is used to solve the nonlinear system. A condition number monitor of matrix is employed in the Anderson acceleration method to achieve better robustness.

Findings

The new scheme is applicable to arbitrary polyhedral grids and has a second-order accuracy. The results of numerical experiments also confirm the positivity-preserving of the discretization scheme.

Originality/value

1. This article presents a new positivity-preserving finite volume scheme for the 3D convection–diffusion equation. 2. The new discretization scheme of convection flux is constructed. 3. A new second-order interpolation algorithm is given to eliminate the auxiliary unknowns in flux expressions. 4. An improved Anderson acceleration method is applied to accelerate the convergence of Picard iterations. 5. This scheme can solve the convection–diffusion equation on the distorted meshes with second-order accuracy.

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来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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