General Framework for Achieving Textbook Multigrid Efficiency: One- dimensional Euler Example

摘要

A general multigrid framework is discussed for obtaining textbook efficiency to solutions of the compressible Euler and Navier-Stokes equations in conservation law form. The general methodology relies on a distributed relaxation procedure to reduce errors in regular (smoothly varying) flow regions; separate and distinct treatments for each of the factors (elliptic and/ or hyperbolic) are used to attain optimal reductions of errors. Near boundaries and discontinuities (shocks) additional local relaxations of the conservative equations are necessary. Example calculations are made for the quasi-one- dimensional Euler equations; the calculations illustrate the general procedure.