Experiments with implicit upwind methods for the Euler equations
Abstract
In the present application of several implicit integration schemes for the onedimensional Euler equations with conservative upwind spatial differencing to a steady discontinuous flow problem, the fastest convergence is obtained with the upwind switching that is furnished by van Leer's (1977) differentiable split fluxes; these easily linearize in time. The trapping of the iterations in a limit cycle with Roe's (1980) nondifferentiable split fluxdifference also occurs in a secondorder scheme with split fluxes, if the matrix coefficients arising in the implicit timelinearization are not properly centered in space. The use of split fluxderived secondorder terms degrades solution accuracy, especially if they are subjected to a limiter for the sake of monotonicity's preservation. The best performance is obtained from secondorder terms computed on the basis of the characteristic variables.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1985
 DOI:
 10.1016/00219991(85)901445
 Bibcode:
 1985JCoPh..59..232M
 Keywords:

 Computational Fluid Dynamics;
 Euler Equations Of Motion;
 Inviscid Flow;
 Shock Waves;
 Spiral Galaxies;
 Steady Flow;
 Convergence;
 Matrices (Mathematics);
 Steady State;
 Stellar Gravitation;
 Fluid Mechanics and Heat Transfer