Abstract:
A new approach to the numerical simulation of gas flows over stationary and moving solid bodies is proposed that makes use of Euler grids not related to the geometry of the body. The bodies are assumed to be rigid and nondeformable, i.e., their elastic properties are ignored. The gas is inviscid and non-heat-conducting and is described by compressible fluid equations. The proposed approach is based on averaging the equations of the original model with respect to a small spatial filter. The resulting system of averaged equations involves an additional quantity, namely, the volume fraction parameter of the solid body, whose spatial distribution provides a digital representation to the body geometry (an analogue of the order function). This system of equations is valid in the entire space. According to this approach, the standard boundary value problem in the gas-occupied region is reduced, in fact, to a Cauchy problem in the entire space. In one dimension, the averaged equations are solved numerically by applying Godunov’s method. In crossed cells discontinuous solution reconstruction is introduced, which leads to a composite Riemann problem, which describes the decay of the initial discontinuity in the presence of a bounding wall. It is proved that the approximation of the numerical flux on the solution of the composite Riemann problem ensures the transport of the order function without numerical dissipation.
Key words:gas dynamics over a moving solid surface, averaged Euler equations, composite Riemann problem, Godunov’s method.
