An Augmented Approach for the Pressure Boundary Condition in a Stokes Flow (Communications in Computational Physics, 2006)
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.
Keywords: Incompressible Stokes equations; pressure boundary condition; augmented method; interface problem; immersed interface method; fast Poisson solver; GMRES method.