A high order MOOD method for compressible Navier-Stokes equations: application to hypersonic viscous flows

A very high-order finite volumes numerical method is designed for the simulation of compressible Navier-Stokes equations on 2D unstructured meshes. This scheme is based on the MOOD methods described for Euler's equations, it is an interesting alternative in the design of a scheme adapted to accurate simulations of flows with discontinuities, in all the domain. The main originality of our method is to include the viscosity/diffusion terms of Navier-Stokes equations. These terms may be discretised with the same accuracy of convection terms, though we will restrict ourselves to second-order here. It permits to treat the hypersonic viscous interactions with high accuracy. Numerical experiments are conducted to demonstrate the performance of the proposed method.