Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations

The derivation of low-storage, explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equa tions via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy effici ency, linear and nonlinear stability, error control reliability, step chang e stability, and dissipation/dispersion accuracy, subject to varying degree s of memory economization. Following van der Houwen and Wray, sixteen ERK p airs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods h ave been tested with not only DETEST, but also with the 1D wave equation. T wo of the methods have been applied to the DNS of a compressible jet as wel l as methane-air and hydrogen-air flames. Derived 3(2) End 4(3) pairs are c ompetitive with existing full-storage methods. Although a substantial effic iency penalty accompanies use of two- and three-register, fifth-order metho ds, the best contemporary full-storage methods can be nearly matched while still saving 2-3 registers of memory. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.