FREE BOUNDARY METHOD FOR COUPLED PROBLEMS OF GAS AND SOLID DYNAMICS

This paper presents a new approach to numerical modeling of gas flow around stationary and moving rigid bodies, allowing for the use of Eulerian grids that are not tied to the geometry of the body. The bodies are assumed to be absolutely rigid and undeformable, with their elastic properties disregarded. The gas is inviscid and non-heat-conducting, described by compressible fluid equations. The proposed approach is based on averaging the equations of the original model over a small spatial filter. This results in a system of averaged equations that includes an additional quantity — the solid volume fraction parameter — whose spatial distribution digitally represents the geometry of the body (analogous to an order function). This system of equations operates across the entire space. Under this approach, the standard boundaryvalue problem within the gas region is effectively reduced to a Cauchy problem over the entire space. For a one-dimensional model, the numerical solution of the averaged equations is considered using Godunov’s method. In intersected cells, a discontinuous solution is introduced, leading to a compound Riemann problem that describes the decay of the initial discontinuity in the presence of a confining wall. It is shown that the approximation of the numerical flux for the compound Riemann problem solution ensures transport of the order function without numerical dissipation.