163 1995 Lars Ferm and Per Lötstedt ferm@tdb.uu.se Two-grid solution of shock problems
The multigrid method is applied to accelerate the convergence to the
steady state of hyperbolic conservation laws using two grid levels.
In supersonic flow with a shock in the solution the convergence
usually slows down with the standard algorithm.
By introducing a restriction, which depends on the residual,
and a corresponding prolongation an improved effect of
the coarse grid is obtained.
The new grid transfer operators are tested on the inviscid Burgers' equation
and the Euler equations in one and two space (1D and 2D) dimensions.
The method is analyzed for Burgers' equation in 1D
and an explanation for the speed-up is given.
In numerical experiments other transfer strategies are compared with
the new one.