On a multi-time step procedure to accelerate time-asymptotic flow calculations

A multi-time step technique to accelerate time-dependent finite-difference calculations to steady-state is proposed. The considered equations are behaving essentially like first order hyperbolic systems, but they also include small second order viscous operators. The proposed method relies on a special implicit differencing procedure making it possible to select a convenient sequence of time steps to get a rapid convergence towards the steady-state solution. The sequence is repeatedly cycled until convergence is obtained. The method is demonstrated on some simple one-dimensional model equations consisting of Burgers equation and a set of isentropic flow equations with added artificial viscosity. A generalization of the method to several space dimensions is briefly touched at.