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

Abstract

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.