Coupling rigid bodies motion with single phase and two-phase compressible flows on unstructured meshes

A simple method is developed to couple accurately translational motion of rigid bodies to compressible fluid flows. Solid rigid bodies are tracked through a Level-Set function. Numerical diffusion is controlled thanks to a compressive limiter (Overbee) in the frame of MUSCL-type-scheme, giving an excellent compromise between accuracy and efficiency on unstructured meshes [9]. The method requires low resolution to preserve solid bodies' volume. Several coupling methods are then addressed to couple rigid body motion to fluid flow dynamics: a method based on stiff relaxation and two methods based on Ghost cells [13] and immersed boundaries. Their accuracy and convergence rates are compared against an immersed piston problem in 1D having exact solution. The second Ghost cell method is shown to be the most efficient. It is then extended to multidimensional computations on unstructured meshes and its accuracy is checked against flow computations around cylindrical bodies. Reference results are obtained when the flow evolves around a rigid body at rest. The same rigid body is then considered with prescribed velocity moving in a flow at rest. Computed results involving wave dynamics match very well. The method is then extended to two-way coupling and illustrated to several examples involving shock wave interaction with solid particles as well as phase transition induced by projectiles motion in liquid-gas mixtures.