A high-order density-based finite volume method for the computation of all-speed flows

In this paper we present a high-order density-based finite-volume framework for all-speed flows. The formulation is based on high-order variable reconstructions performed using Moving Least Squares approximations. In particular, we show that combining high-order discretization schemes with low-Mach fixes, it is possible to remove the grid dependency problem at low Mach numbers on both structured and unstructured grids. In order to maintain the accuracy and the robustness of the numerical method at transonic conditions, different procedures are proposed, based on the use of a selective limiting.