Coupling Stokes--Darcy Flow with Transport
Coupling Stokes--Darcy Flow with Transport
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DOI：
10.1137/080732146
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
D. Vassilev;I. Yotov
中科院分区：
文献类型：
--
作者：
D. Vassilev;I. Yotov
讨论了描述Stokes-Darcy流动系统中化学物质输运的数学和数值模型。在Stokes区域采用经典有限元方法求解流动方程，在Darcy区域采用混合有限元方法求解流动方程。输运方程的求解采用局部间断Galerkin(LDG)方法。处理Stokes方程和Darcy方程之间耦合的模型在文献中得到了广泛的讨论。本文主要研究输运方程的逼近问题。分析了LDG格式的稳定性，证明了一个先验误差估计。文中给出了几个数值算例，验证了理论和方法的有效性。
A mathematical and numerical model describing chemical transport in a Stokes–Darcy flow system is discussed. The flow equations are solved through domain decomposition using classical finite element methods in the Stokes region and mixed finite element methods in the Darcy region. The local discontinuous Galerkin (LDG) method is used to solve the transport equation. Models dealing with coupling between Stokes and Darcy equations have been extensively discussed in the literature. This paper focuses on the approximation of the transport equation. Stability of the LDG scheme is analyzed, and an a priori error estimate is proved. Several numerical examples verifying the theory and illustrating the capabilities of the method are presented.