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

Zhilin Li*, Kazufumi Ito, Ming-Chih Lai

*Corresponding author for this work

Research output: Contribution to journalArticle

45 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)622-635
Number of pages14
JournalComputers and Fluids
Volume36
Issue number3
DOIs
StatePublished - 1 Mar 2007

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