Higher order accurate and high-resolution implicit upwind finite volume scheme for solving Euler/Reynolds-averaged Navier-Stokes equations

A new type of third order upwind finite volume implicit scheme is proposed for solving two/three dimensional Euler/Reynolds averaged Navier Stokes equations for steady flow. The fundamental form of the implicit scheme is based on the LU TVD finite volume scheme with the hybrid flux splitting technique. The third order ENN scheme's numerical flux is used to calculate the inviscid terms of Navier Stokes equations. A fourth order accurate Symmetric compact difference is applied to its viscous terms. The Baldwin Lomax turbulence model is used to calculate the turbulent viscosity. Numerical experiments suggest that the proposed scheme not only has a fairly rapid convergence rate, but also can generate a highly resolved approximation to the numerical solution.