用基本解交替法求解布林克曼方程的考奇问题

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED
Andreas Karageorghis, Daniel Lesnic
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引用次数: 0

摘要

在本文中,我们打算提出并解决支配多孔介质中流体流动的布林克曼方程的考奇问题。物理情景对应的情况是,流体领域的部分边界是敌对的或无法进入的,而在边界的其余友好部分,我们规定或测量流体速度和牵引力。由此产生的数学公式导致了一个线性但难以解决的问题。我们开发了一种基于求解两个混合直接问题子序列的收敛算法。直接求解器基于基本解法,这是一种无网格边界配位方法。由于所研究的问题是求解困难的问题,因此根据差异原则,在输入测量数据所含噪声量达到一定临界值时停止迭代过程,以防止出现不稳定性。对二维和三维问题的精确数据和噪声数据进行反演的结果表明,所提出的数值算法具有收敛性和稳定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Solution of the Cauchy problem for the Brinkman equations using an alternating method of fundamental solutions

Solution of the Cauchy problem for the Brinkman equations using an alternating method of fundamental solutions

In this paper, we intend to formulate and solve Cauchy problems for the Brinkman equations governing the flow of fluids in porous media, which have never been investigated before in such an inverse formulation. The physical scenario corresponds to situations where part of the boundary of the fluid domain is hostile or inaccessible, whilst on the remaining friendly part of the boundary we prescribe or measure both the fluid velocity and traction. The resulting mathematical formulation leads to a linear but ill-posed problem. A convergent algorithm based on solving two sub-sequences of mixed direct problems is developed. The direct solver is based on the method of fundamental solutions which is a meshless boundary collocation method. Since the investigated problem is ill-posed, the iterative process is stopped according to the discrepancy principle at a threshold given by the amount of noise with which the input measured data is contaminated in order to prevent the manifestation of instability. Results inverting both exact and noisy data for two- and three-dimensional problems demonstrate the convergence and stability of the proposed numerical algorithm.

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来源期刊
Numerical Algorithms
Numerical Algorithms 数学-应用数学
CiteScore
4.00
自引率
9.50%
发文量
201
审稿时长
9 months
期刊介绍: The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.
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