A particle kinetic approach to compressible inviscid gas dynamics with embedded boundaries

Benjamin Keen, University of Michigan

An attractive way of realizing complex boundary geometries in volume-of-fluid hydrodynamics calculations is to embed the boundary in an otherwise regular cartesian grid. This results in cut cells of arbitrarily small volume, which via the Courant-Friedrichs-Lewy (CFL) restriction makes the stable timestep arbitrarily small.

There are already ways of overcoming this stability restriction in the small cells, such as cell merging and flux redistribution. This is a different way of overcoming the ‘small cell stability problem’, in the case of reflecting boundaries, through a simple modification of a conservative Boltzmann type scheme for solving the Euler equations of compressible inviscid flow. The basic idea offers good prospects of practical stable extension to the case where the embedded geometry moves relative to the regular mesh.

Abstract Author(s): Benjamin Keen