具有时变源项的长时间瞬态扩散的一种新的时空搭配求解器

IF 4.2 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Wenzhi Xu , Zhuojia Fu , Qiang Xi , Qingguo Liu , Božidar Šarler
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引用次数: 0

摘要

针对源项随时间变化的二维和三维长时间扩散问题,提出了一种新的时空搭配求解器。本文采用一系列半解析时空基本解来近似时变扩散方程的解,只对初始条件和边界条件进行节点离散化。该方法避免了传统时间离散方法(拉普拉斯/傅立叶变换和时间步进格式等)中数值拉普拉斯/傅立叶逆变换或时间步长选择的问题。为了处理时变源项,将多重互易方法从空间域扩展到时空域,通过一系列微分算子将非齐次控制方程转化为高阶偏微分方程,而无需在时空域进行额外的离散化。算例验证了所提求解方法的可行性、有效性和准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A novel spatial-temporal collocation solver for long-time transient diffusion with time-varying source terms
In this paper, a novel spatial-temporal collocation solver is proposed for the solution of 2D and 3D long-time diffusion problems with source terms varying over time. In the present collocation solver, a series of semi-analytical spatial-temporal fundamental solutions are used to approximate the solutions of the time-dependent diffusion equations with only the node discretization of the initial and boundary conditions. This approach avoids the numerical inverse Laplace/Fourier transformations or the selection of the time-step size in the traditional time discretization methods (Laplace/Fourier transformations and time-stepping scheme, etc.). To treat with the time-varying source terms, an extension of the multiple reciprocity method from the spatial domain to the spatial-temporal domain is achieved, which converts the nonhomogeneous governing equation into a high-order partial differential equation via a series of differential operators without the need for additional discretization in the spatial-temporal domain. Several numerical examples validate the feasibility, efficiency and accuracy of the proposed solver.
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来源期刊
Engineering Analysis with Boundary Elements
Engineering Analysis with Boundary Elements 工程技术-工程:综合
CiteScore
5.50
自引率
18.20%
发文量
368
审稿时长
56 days
期刊介绍: This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.
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