A directional ghost-cell immersed boundary method for incompressible flows

Abstract

This paper describes an efficient ghost-cell immersed boundary method for incompressible flow simulations. The method employs a locally directional extrapolation scheme along all discretization directions for the ghost values. Additionally, it involves fictitious discrete boundary forcing terms instead of the ghost values in the governing equations. In this way, the boundary is represented more accurately than in prior IBMs and it is possible to fulfill the divergence-free condition. When combined with high-order spatial discretization schemes, the IBM order is reduced locally near the immersed boundary in a step-wise manner. In this way, the method delivers more compact stencils and is able to deal with sharp interfaces. By handling the distance from the ghost point to the boundary carefully, the proposed method delivers lower truncation errors than standard IBM, with clean (persistent) convergence rate and enhanced stability. The parallel implementation of this approach is straightforward. Its accuracy has been checked by considering a variety of test cases, including irregular, three-dimensional, and moving boundaries. The local accuracy for the proposed method is formally second order, and is measured to be close to this value using numerical tests.