Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method (Advances in Applied Mathematics and Mechanics, 2012)
A local domain-free discretization-immersed boundary method (DFD-IBM)is presented in this paper to solve incompressible Navier-Stokes equationsin the primitive variable form. Like the conventional immersed boundary method(IBM), the local DFD-IBM solves the governing equations in the whole domain includingexterior and interior of the immersed object. The effect of immersed boundaryto the surrounding fluids is through the evaluation of velocity at interior andexterior dependent points. To be specific, the velocity at interior dependent pointsis computed by approximate forms of solution and the velocity at exterior dependentpoints is set to the wall velocity. As compared to the conventional IBM, thepresent approach accurately implements the non-slip boundary condition. As a result,there is no flow penetration, which is often appeared in the conventional IBMresults. The present approach is validated by its application to simulate incompressibleviscous flows around a circular cylinder. The obtained numerical resultsagree very well with the data in the literature.