Least-squares finite element models of two-dimensional compressible flows

We present numerical simulation results for the compressible Euler equations and compressible Navier-Stokes equations using least-squares finite element models. Alternative least-squares formulations are first exemplified by a Poisson problem and ideas extended to the Euler and Navier-Stokes equations. For the compressible Navier-Stokes equations we introduce velocity gradients and heat fluxes as additional primary variables to arrive at an equivalent first-order system. The least-squares models developed herein are found to be effective for the high- and low-speed compressible flow regimes. 2003 Elsevier B.V. All rights reserved.

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