A Direct Discontinuous Galerkin Method with Interface Correction for the Compressible Navier-Stokes Equations on Unstructured Grids (Advances in Applied Mathematics and Mechanics, 2018)
Since the original DDG method has been introduced by Liu et al. [8] in 2009,a variety of DDG type methods have been proposed and further developed. In thispaper, we further investigate and develop a new DDG method with interface correction(DDG (IC)) as the discretization of viscous and heat fluxes for the compressibleNavier-Stokes equations on unstructured grids. Compared to the original DDGmethod, the newly developed DDG (IC) method demonstrates its superior in deliveringthe optimal order of accuracy under demanding situations. Strategies in extensionand application of this newly developed DDG (IC) method for solving the compressibleNavier-Stokes equations and special treatments designed for handling boundaryviscous fluxes are presented and examined in this work. The performance of the newDDG method with interface correction is carefully evaluated and assessed through anumber of typical test cases. Numerical experiments show that the new DDG methodwith interface correction can achieve the optimal order of accuracy on both uniformstructured grids and nonuniform unstructured grids, which clearly indicates its potentialfor further applications of real engineering practices.