Higher order accuracy for upwind methods by using the compatibility equations

A new algorithm has been developed for obtaining higher order accuracy in upwind schemes for the Euler and Navier-Stokes equations. In this method, the compatibility relations for the Euler equations are used to construct formulas for the higher order interpolates. Using these formulas, computed results are obtained for steady, inviscid flow through a nozzle and also steady, inviscid and viscous flow over an airfoil. These results are compared with results obtained by using a minmod limiter function. The comparisons show improved accuracy throughout the flow field with the use of the compatibility equations.