Abstract

In this paper we construct a MAC methods for coupled Stokes–Darcy problems on non-uniform staggered grids using the covolume integration on the interface. The inf–sup condition and the stability for both velocity and pressure for MAC scheme have been established. Then we analyze the convergence of the scheme and obtain the second order super-convergence in L2 norm for both velocity and pressure of the Stokes flow and Darcy flow. We also obtain the second order super-convergence for some terms of H1 norm of the Stokes velocity, and the other terms of H1 norm are second order super-convergence on uniform grids. Numerical experiments using the MAC scheme show agreement of the numerical results with theoretical analysis.

中文翻译：

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非均匀网格上耦合Stokes-Darcy方程的MAC格式

摘要

在本文中，我们使用接口上的卷积积分，构造了非均匀交错网格上耦合Stokes-Darcy问题的MAC方法。已经建立了MAC方案的注入条件和速度和压力的稳定性。然后，我们对该方案的收敛性进行了分析，并获得了斯托克斯流和达西流的速度和压力在L2范数中的二阶超收敛。我们还获得了Stokes速度H1范数的某些项的二阶超收敛性，而H1范数的其他项是均匀网格上的二阶超收敛性。使用MAC方案进行的数值实验表明数值结果与理论分析一致。