Pseudo-time algorithms for the Navier-Stokes equations

R. C. Swanson*, E. Turkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This enables the time-step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.

Original languageEnglish
Pages (from-to)321-333
Number of pages13
JournalApplied Numerical Mathematics
Issue number3-5
StatePublished - Oct 1986


FundersFunder number
National Aeronautics and Space Administration


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