Explicit Third Order Compact Upwind Difference Schemes for13; Compressible Flow Calculations

A compact upwind difference operator is used to generate formally third order accurate spatial discretizations for the inviscid flux terms of the Euler equations governing compressible fluid flow. A notable feature of the present work is that currently well known first order upwind fluxes such as that of Murman or Roe have been used interchangeably. A Runge-Kutta time stepping algorithm is combined with the high order spatial discretization to produce effective integration schemes for the Euler equations that may be used for both steady and unsteady computations