Iterative implementation of an implicit-explicit hybrid scheme for hydrodynamics
Iterative implementation of an implicit-explicit hybrid scheme for solving the Euler equations is described. The scheme is of the Godunov-type in both explicit and implicit regimes, is conservative, and is accurate to the second order in both space and time for all Courant numbers. Only a single level of iterations is involved in the implementation, which solves both the implicit relations arising from upstream centered differences for all wave families and the nonlinearity of the Euler equations. The number of iterations required to reach a convergent solution may be significantly reduced by the introduction of the multicolors proposed in this paper.
scientific article; zbMATH DE number 881882