Sixth Mississippi State Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 193-210.

An augmented IIM-level set method for Stokes equations with discontinuous viscosity

Zhilin Li, Sharon R. Lubkin, Xiaohai Wan

Abstract:
A finite difference method is proposed for incompressible Stokes equations with discontinuous viscosity. The method combines the augmented immersed interface method with a level set representation of the interface on a uniform Cartesian grid. In the proposed method, augmented interface variables are introduced along the interface and be solved by the GMRES iterative method. The augmented approach allows fast Poisson solvers to be used and therefore is very efficient. Numerical examples including two moving interface problems are presented.

Published February 28, 2007.
Math Subject Classifications: 65M06, 65M12, 76T05.
Key Words: Incompressible Stokes equations; discontinuous viscosity; interface problem; immersed interface method; level set method; fast Poisson solver, GMRES.

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Zhilin Li
Center for Research in Scientific Computation
& Department of Mathematics
North Carolina State University
Raleigh, NC 27695-8205, USA
email: zhilin@math.ncsu.edu
Sharon R. Lubkin
Center for Research in Scientific Computation
& Department of Mathematics
North Carolina State University
Raleigh, NC 27695-8205, USA
email: lubkin@math.ncsu.edu
Xiaohai Wan
Biomathematics Graduate Program
& Department of Mathematics
North Carolina State University
Raleigh, NC 27695-8203, USA
email: xwan@unity.ncsu.edu

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