Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy Problems
Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy Problems
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DOI：
10.1007/s10915-004-4147-3
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发表时间：
2005
影响因子：
2.5
通讯作者：
B. Rivière
中科院分区：
文献类型：
--
作者：
B. Rivière
模拟地表和地下水流之间的相互作用是一个具有挑战性的环境问题。其中一个例子是模拟污染物通过河流进入含水层。在数学上，这个复杂的问题可以用Stokes和Darcy方程的耦合系统来描述，本文的目的是建立和分析Stokes和Darcy耦合问题的间断有限元方法。物理域被分解成两个区域：填充由Stokes方程建模的不可压缩流体的区域和由达西定律建模的多孔介质区域。界面条件包括Beavers-Joseph-Saffman条件、通量连续性和力的平衡。界面处的网格匹配条件可以放宽。未知量，即流体区域中的流体速度和压力，以及多孔介质中的流体压力，由不同阶的完全不连续多项式近似。这里考虑的间断Galerkin（DG）方法是基于
Modeling the interaction between surface and subsurface flow is a challenging environmental problem. One such example is the simulation of transport of contaminants through rivers into the aquifers. Mathematically, this complex problem can be modeled by the coupled system of Stokes and Darcy equations.The aim of this paper is to formulate and analyze a discontinuous finite element method for the coupled Stokes and Darcy problems. The physical domain is decomposed into two regions: the region filled with an incompressible fluid modeled by the Stokes equations and the porous medium region modeled by Darcy’s law. The interface conditions consist of the Beavers–Joseph–Saffman condition, the continuity of flux and the balance of forces. The matching condition of meshes at the interface can be relaxed. The unknowns, namely the fluid velocity and pressure in the fluid region, and the fluid pressure in the porous medium, are approximated by totally discontinuous polynomials of different order. The discontinuous Galerkin (DG) methods considered here, are based on the