Design of optimally smoothing multistage schemes for the Euler equations
Abstract
A recently derived local preconditioning of the Euler equations is shown to be useful in developing multistage schemes suited for multigrid use. The effect of the preconditioning matrix on the spatial Euler operator is to equalize the characteristic speeds. When applied to the discretized Euler equations, the preconditioning has the effect of strongly clustering the operator's eigenvalues in the complex plane. This makes possible the development of explicit marching schemes that effectively damp most highfrequency Fourier modes, as desired in multigrid applications. The technique is the same as developed earlier for scalar convection schemes: placement of the zeros of the amplification factor of the multistage scheme in locations where eigenvalues corresponding to highfrequency modes abound.
 Publication:

Communications in Applied Numerical Methods
 Pub Date:
 October 1992
 Bibcode:
 1992CANM....8..761V
 Keywords:

 Euler Equations Of Motion;
 Finite Difference Theory;
 Optimization;
 Upwind Schemes (Mathematics);
 Eigenvalues;
 Flow Velocity;
 Fluid Mechanics and Heat Transfer