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

A high-order accurate explicit scheme is proposed for solving Euler/Reynolds-averaged Navier-Stokes equations for steady and unsteady flows, respectively. Baldwin-Lomax turbulence model is utilized to obtain the turbulent viscosity. For the explicit scheme, the Runge-Kutta time-stepping methods of third orders are used in time integration, and space discretization for the right-hand side (RHS) terms of semi-discrete equations is performed by third-order ENN scheme for inviscid terms and fourth-order compact difference for viscous terms. Numerical experiments suggest that the present scheme not only has a fairly rapid convergence rate, but also can generate a highly resolved approximation to numerical solution, el en to unsteady problem.