The Multigrid / τ - extrapolation technique applied to the IBM
نویسنده
چکیده
The Immersed Boundary Method (IBM), originally developed by C.S. Peskin [Pes72], is a very practical method of simulating fluid-structure interactions. It combines Eulerian and Lagrangian descriptions of flow and moving elastic boundaries using Dirac delta functions. Incompressible Navier-Stokes and Elasticity theory can be unified by the same set of equations to get a combined model of the interaction. There are numerous applications of the IBM in Bio-Engineering or in more general Computational Fluid Dynamics applications. We present a numerical study of the accuracy and computational cost of the method, in the frame of finite-differences, based on the implementation of several mathematical tools such as multigrid solvers, τ -extrapolation technique, multilevel discretization and more generally numerical methods for differential equations with singular source terms. These implementations are being made on test-cases that are relevant for the IBM applications, keeping in mind that we want to keep the simplicity of the method.
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