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.