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

Authors: Rodolphe Turpault; Thanh-Ha Nguyen-Bui

Addresses: Institut de Mathematiques de Bordeaux, Bordeaux-INP, 351 Cours de la libération, 33405 Talence Cedex, France ' CELIA, UMR 5107, CNRS – University of Bordeaux – CEA, 351 Cours de la libération, 33405 Talence Cedex, France

Abstract: 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.

Keywords: numerical scheme; MOOD methods; high-order; viscous fluids; supersonic; discontinuities; simulations.

DOI: 10.1504/PCFD.2019.10024489

Progress in Computational Fluid Dynamics, An International Journal, 2019 Vol.19 No.6, pp.337 - 345

Received: 31 Aug 2017
Accepted: 03 May 2018

Published online: 23 Oct 2019 *

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