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An augmented approach for Stokes equations with a discontinuous viscosity and singular forces

机译：具有不连续粘度和奇异力的Stokes方程的增强方法

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摘要

For Stokes equations with a discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, it is known that the pressure is discontinuous and the velocity is non-smooth. It has been shown that these discontinuities are coupled together, which makes it difficult to obtain accurate numerical solutions. In this paper, a new numerical method that decouples the jump conditions of the fluid variables through two augmented variables has been developed. The GMRES iterative method is used to solve the Schur complement system for the augmented variables that are only defined on the interface. The augmented approach also rescales the Stokes equations in such a way that a fast Poisson solver can be used in each iteration. Numerical tests using examples that have analytic solutions show that the new method has average second order accuracy for the velocity in the infinity norm. An example of a moving interface problem is also presented.
机译：对于在任意界面上具有不连续粘度或/和沿界面的奇异力的斯托克斯方程，已知压力是不连续的，速度是不平滑的。已经显示出这些不连续性被耦合在一起，这使得难以获得精确的数值解。在本文中，开发了一种新的数值方法，该方法通过两个扩展变量解耦流体变量的跳跃条件。 GMRES迭代方法用于求解Schur补码系统中仅在接口上定义的增强变量。增强方法还重新缩放了Stokes方程，以便可以在每次迭代中使用快速的Poisson求解器。使用具有解析解的示例进行的数值测试表明，该新方法对无穷大范数中的速度具有平均二阶精度。还提供了移动界面问题的示例。

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