A fast immersed interface method for solving Stokes flows on irregular domains

We present a fast immersed interface method for solving the steady Stokes flows involving the rigid boundaries. The immersed rigid boundary is represented by a set of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundary, singular forces at the rigid boundary are applied on the fluid. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are approximated using the cubic splines. The strength of singular forces is determined by solving a small system of equations via the GMRES method. The Stokes equations are discretized using finite difference method with the incorporation of jump conditions on a staggered Cartesian grid and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate Stokes flows on irregular domains.

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