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Title: An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Authors: Tan, Z. 
Lim, K.M. 
Khoo, B.C. 
Keywords: CG-Uzawa method
Deformable interface
Front tracking
Immersed interface method
Incompressible Stokes equations
Irregular domains
Rigid boundaries
Singular force
Issue Date: 1-Oct-2009
Citation: Tan, Z., Lim, K.M., Khoo, B.C. (2009-10-01). An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries. Journal of Computational Physics 228 (18) : 6855-6881. ScholarBank@NUS Repository.
Abstract: We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid boundaries are represented by a number of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundaries, singular forces are applied on the fluid at these boundaries. The strength of singular forces at the rigid boundary is determined by solving a small system of equations. For the deformable interfaces, the forces that the interface exerts on the fluid are calculated from the configuration (position) of the deformed interface. The jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed/moving interfaces and rigid boundaries. These forces are interpolated using cubic splines and applied to the fluid through the jump conditions. The positions of the deformable interfaces are updated implicitly using a quasi-Newton method (BFGS) within each time step. In the proposed method, the Stokes equations are discretized via the finite difference method on a staggered Cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible Stokes flows with fixed/moving interfaces on irregular domains. © 2009 Elsevier Inc. All rights reserved.
Source Title: Journal of Computational Physics
ISSN: 00219991
DOI: 10.1016/
Appears in Collections:Staff Publications

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