Immersed boundary methods for compressible laminar flows

Immersed boundary methods (IB) are a set of methods to deal with non-body conforming grids. This requires forcing the boundary conditions in the vicinity of the immersed surface. In this work, the embedded object is represented as a set of line segments along with their outward unit normal vectors. The flow domain is categorised into field cells, band cells or interior cells using a signed distance based approach. Although IB methods have been widely used for incompressible flows, it's application to high speed flows is relatively less. The proposed work attempts to construct an IB method suitable for compressible flow applications. Velocity boundary conditions are applied using an inverse distance based approach near no-slip walls and a signed distance based approach for slip walls. Different flow problems are simulated: expansion fan, supersonic flow past ramp channel and supersonic flow past NACA0012 airfoil which are inviscid simulations, subsonic viscous laminar flow past a ramp channel and flow past a cylinder (to simulate Von Karman vortex streets) which are viscous simulations. In each case, a comparison is made with simulations using body fitted grids or experimental data to validate the solution.