Spectral (finite) volume method for conservation laws on unstructured grids VI: Extension to viscous flow

In this paper, the spectral volume (SV) method is extended to solve viscous flow governed by the Navier–Stokes equations. Several techniques to discretize the viscous fluxes have been tested, and a formulation similar to the local discontinuous Galerkin (DG) approach developed for the DG method has been selected in the present study. The SV method combines two key ideas, which are the bases of the finite volume and the finite element methods, i.e., the physics of wave propagation accounted for by the use of a Riemann solver and high-order accuracy achieved through high-order polynomial reconstructions within spectral volumes. The formulation of the SV method for a 2D advection-diffusion equation and the compressible Navier–Stokes equations is described. Accuracy studies are performed using problems with analytical solutions. The solver is used to compute laminar viscous flow problems to shown its potential.