Hybrid Multigrid DG/FV Methods for Viscous Turbulent Flows

Abstract

This chapter presents the development of a hybrid technique for coupling Discontinuous Galerkin (DG) and Finite Volume methods for compressible turbulent flow computations in a block-structured code with the RANS system of equations. This code developed at ONERA has been initially built from the following numerical tools : multi-domain approach using structured grids with patched or overlapping interfaces, cell-centered finite volume discretization, space-centered Jameson scheme, multigrid and implicit acceleration techniques (IRS or LDU), boundary condition treatment based on characteristic relations. It has been validated for the simulation of inviscid and turbulent complex internal and external flow configurations and the Finite Volume (FV) functionalities have been integrated in the elsA software environment developed at ONERA which is actually used both by aerospace manufacturers and research laboratories. The code structure enables to re-use as much as possible existing multiblock and multigrid functionalities for the DG method. The RANS system of equations coupled with a kω turbulence model are reformulated as a first-order system in space using the mixed DG approach. The boundary condition treatment is performed through a reconstruction of the solution at the physical boundary which avoids the use of a ghost cell technique and improves stability. This method allows space discretization with overlapping and non-matching multidomains as well as high order polynomial approximations of the solution. Numerical examples for 3D inviscid and turbulent flows are presented to demonstrate the capacity of the method, as well as hybrid multidomain multigrid computations.