Immersed boundary approaches for fluid flows: Challenges and Applications

Abstract: We discuss our experiences with two different classes of immersed boundary (IB) approaches for fluid flows viz. sharp interface and diffuse interface approaches. An overview of both the approaches is presented with emphasis on their specific implementation in a finite-volume framework. We focus on the sharp-interface approach for both inviscid and viscous compressible flows while the diffuse interface approach is applied to genuinely incompressible flows. The advantages and drawbacks of both sharp and diffuse interface approaches for flows with moving bodies and their ability to handle Dirichlet and Neumann BCs are discussed. A few applications of these approaches in hypersonic compressible and multi-phase incompressible flows are described and some of the prominent issues and challenges which we are currently faced with are highlighted.