Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

A low diffusion E-CUSP (LDE) scheme for preconditioned Navier–Stokes equations is developed. The LDE scheme with high-order WENO reconstruction and high order difference scheme for viscous terms is used to simulate several flows at various speed from low speed natural convection to supersonic flows. The unfactored implicit Gauss–Seidel relaxation scheme, in which the preconditioned Roe’s matrices are used, is used for time integration. Numerical results are presented to show efficiency, accuracy and robustness of the new preconditioning scheme.

► A low diffusion E-CUSP (LDE) scheme for preconditioned Navier–Stokes equations is developed.
► Fifth order weighted essentially non-oscillatory scheme with a 4th order central differencing is used.
► Implicit time marching scheme with Gauss–Seidel line relaxation is implemented.
► The new method can treat flows at all speeds from incompressible to supersonic flows with shock waves.