Commun. Comput. Phys., 1 (2006), pp. 874-885.


An Augmented Approach for the Pressure Boundary Condition in a Stokes Flow

Zhilin Li 1*, Xiaohai Wan 2, Kazufumi Ito 1, Sharon R. Lubkin 1

1 Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA.
2 Biomathematics Graduate Program & Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8203, USA.

Received 2 October 2005; Accepted (in revised version) 28 February 2006

Abstract

An augmented method is proposed for solving stationary incompressible Stokes equations with a Dirichlet boundary condition along parts of the boundary. In this approach, the normal derivative of the pressure along the parts of the boundary is introduced as an additional variable and it is solved by the GMRES iterative method. The dimension of the augmented variable in discretization is the number of grid points along the boundary which is O(N). Each GMRES iteration (or one matrix-vector multiplication) requires three fast Poisson solvers for the pressure and the velocity. In our numerical experiments, only a few iterations are needed. We have also combined the augmented approach for Stokes equations involving interfaces, discontinuities, and singularities.


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Key words: Incompressible Stokes equations; pressure boundary condition; augmented method; interface problem; immersed interface method; fast Poisson solver; GMRES method.


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Correspondence to: 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
 

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