IMMERSED BOUNDARY METHODS FOR COMPRESSIBLE FLOWS

Abstract

A novel flux correction-based immersed boundary method (FC-IBM), a local domain-free discretization (LDFD) method and a local DFD-based immersed boundary method (LDFD-IBM) were introduced to simulate compressible flows in a Cartesian grid-based adaptive solver. For the first time, we are able to implement the widely adopted IBM concept for incompressible flows to solve compressible inviscid flows.

The proposed methods have been validated comprehensively by simulating compressible inviscid flows at different conditions with various irregular boundaries. The Adaptive Mesh Refinement (AMR) technique is implemented to improve the computational efficiency and solution accuracy. The numerical results obtained demonstrated the new methods to be accurate and efficient. However, numerical viscosity is noticed in the FC-IBM and LDFD-IBM implementation and needs to be further studied.

The methods were implemented in a 3D adaptive solver and the results for the primary tests are promising. The adaptive solver was extended to simulate viscous flows as well.