An improved IP scheme for compressible Navier-Stokes equation

Abstract

Based on the internal penalty discontinuous Galerkin method (IP-DG), an improved discretization method is proposed to solve the viscosity term of Navier-Stokes equation. The improved method can eliminate the calculation process of intermediate variables and variable gradients, and effectively improve the calculation efficiency. Because the calculation process of convection flux, viscous flux, and lifting operators can be performed at the current integration point, there is no need to calculate the derivative of the viscosity term with respect to the variable gradient, the improved method has very good local characteristics, and is easy to extend to other PDEs. The Couette flow verifies the design accuracy of the improved method, and the cavity flow problem proves the effectiveness of the method for viscous flow simulation. The example of the flow around a sphere shows that this method also has a good performance for three-dimensional problems.