An efficient semi-implicit time accurate scheme for unsteady viscous flow on dynamic grids

Abstract

This paper presents a semi-implicit method for efficient and high-order time-accurate computations for unsteady viscous hypersonic flows over fixed or moving bodies using Navier-Stokes equations. The equations are discretized in space using a second-order TVD scheme on moving structured grids. If explicit schemes are used to advance the equations in time, the small grid sizes in the wall-normal direction in the boundary layers imposed severe restrictions on the time steps. In the current method, the spatial discretization of the governing equations is separated into stiff terms involving derivatives along the wall-normal direction and nonstiff terms for the rest of the equations. The split equations are then advanced in time using second- and third-order semi-implicit Runge-Kutta schemes so that the nonstiff streamwise terms are treated by explicit Runge-Kutta methods and stiff wall-normal terms are simultaneously treated by implicit Runge-Kutta methods. The semi-implicit method leads to block pentagonal diagonal systems of implicit equations that can be solved efficiently. (Author)