Numerical solution of two-dimensional compressible Navier-Stokes equations using rational Runge-Kutta method

In this paper, the method of lines approach is proposed for solving viscous compressible flows. In the method of lines, semi-discretization of independent variables reduces the governing partial differential equations to a set of ordinary differential equations (ODEs) in time, which are integrated by using an appropriate time integration scheme. This separation of the space and time discretization assures a steady state solution independent of time step. As a time stepping procedure, we propose to use rational Runge-Kutta (RRK) method. The RRK method proposed by Wambecq [1] is fully explicit, requires no matrix inversion, and is stable at much larger time step than the usual explicit methods. The RRK method has been applied to solve both the Euler [2,3] and the Navier-Stokes equations [4,5]. Local time stepping and implicit residual averaging [6] techniques have been employed to accelerate convergence of solution to steady state.