DEVELOPMENT AND APPLICATION OF AN IMMERSED BOUNDARY-FICTITIOUS DOMAIN MULTIGRID PRECONDITIONER FOR A NAVIER-STOKES EQUATION IN COMPLEX GEOMETRIES

Abstract

Most of the industrial applications involve flows in complex geometries. Numerical simulation of such flows is based on either of the following three applications: 1) Unstructured grids 2) Body fitted structured grids 3) Structured Cartesian grids. The first two approaches involve a significant investment of time and resources for grid generation. In contrast, the structured cartesian grid generation is very straight forward. In past, the main obstacle to use this approach has been in the inaccuracies in the solution resulting from curved boundary segments and boundary conditions prescribed there. Recently developed immersed boundary technologies alleviate this situation by special handling of cells on curved boundary. However, due to complex geometry, only simple iterative solvers such as successive over relaxation (SOR) can be used for the solution of poisons equation for pressure correction. Since the solution of pressure in the pressure equation accounts for 80 to 95% of the computation time at each time step, it imposes severe restriction on the efficiency of flow solver. We have developed a immersed boundary-fictitious domain approach which would allow us to use fast poisson solvers such as multigrid for the solution of the pressure Poisson equation, and there by obtain a robust and efficient flow solver