Steady state computations for wave propagation problems

The behavior of difference approximations of hyperbolic partial differential equations as time t goes to infinity is studied. The rate of convergence to steady state is analyzed theoretically and experimentally for the advection equation and the linearized Euler equations. The choice of difference formulas and boundary conditions strongly influences the rate of convergence in practical steady-state calculations. In particular it is shown that upwind difference methods and characteristic boundary conditions have very attractive convergence properties.