New weighted end-strongly compact difference schemes and dual-time method for the solution of the unsteady flows on unstructured grids

A new shock capturing finite difference dual-time method of weighted END and strongly compact difference-based finite-volume type is presented for solving three-dimensional, unsteady Navier-Stokes equations on unstructured grids. The present numerical method has the second order accuracy in time and no than the third order accuracy in space. The convective numerical flux functions of the fundamental governing equations are estimated using third order weighted END scheme and strongly compact scheme, based on an approximate Riemann solver. The viscosity items of Navier-Stokes equations are estimated using fourth order accurate strongly compact scheme. In the current paper numerical results obtained by using present method are compared to experimental data. The results indicate the present method gives good agreement with the measured values. In summary, the present method has high efficiency and high resolution to capture shock wave and contact surface.