Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

Summary A preconditioned dual-time algorithm has bee:: im-plemented in the OVERFLOW code. The approachfollows the method of Buelow et al. to tailor the formu-lation within the diagonalized solution procedure usedin the OVERFLOW code. Modifications of the pre-The particle trace at an instance in time for a jet at M = 0.13 in a hi : 0.013 cross flowResidual History Log 10(L2 norm of delta Q)r T • r5816400 16600 16800 17000 17200 17400Time Step Number Fig. 10 The residual with respect to time step forthe jet in cross flowconditioning selection to account for unsteady scaleshave also been included. The method significantly en-hances the capability of the code, enabling it to handleunsteady flows over a wide range of Math numbers andtime scales. Specifically, the preconditioned dual-timemethod enhances accuracy by improving the sealingof the artiflcal dissipation terms used in the numer-ical discret.ization procedure and improves efficiencyby optimizing the number of sub-iterations requiredat each physical time step. For low Mach nmnber, lowfrequency problems, in particular, significant savingsin CPU time are possible.The enhancements made possible by the method aredemonstrated for both simple and practical flowfields.The simple test problems include the propagation ofa Lamb vortex in an straight channel and the flow-field of an impulsively started plate. Computationalresults reveal that the dual-time scheme with unsteadypreconditioning provides optimal sub-iteration conver-gence for all choices of time step size and Mach num-ber. Moreover, improved accuracy is also obtainedwith the method.Preliminary computations of a round jet it: a lowMach crossflow with ground effect have also been per-10American Institute of Aeronautics and Astronautics