A Parallel High-Order Implicit Algorithm for Compressible Navier-Stokes Equations

In recent years, direct numerical simulation (DNS) has become a powerful tool to study the stability and transition of compressible boundary layers. The difficulty in using explicit methods for DNS of hypersonic flow is the limitation of the temporal steps since the Navier-Stokes equations are stiff for explicit numerical schemes. Due to the progress in computer techniques in recent years, one way to overcome the limitation of small time steps in explicit method is by using distributed memory computers. However, a short marching step still can not be avoided during the computation due to stability limitation. Implicit method is considered to improve the efficiency of solving NavierStokes equations. In this paper, we extend our previous work to develop and validate the new high-order parallelized semi-implicit shock-fitting code solving the compressible Navier-Stokes equations. Divide and conquer method is used as a start point for the solution of the big banded matrix. The new parallel semi-implicit code has been tested in solving a 2-D convection-diffusion model equation first. Efficiency and accuracy are studied. Several test cases, which include the numerical simulations of the stability of 3-D supersonic Couette flow, and hypersonic boundary layer receptivity to freestream acoustic waves over 3-D blunt wedge, are used to evaluated the efficiency and accuracy of the new parallelized code.