Narrow Results

The convection and diffusion processes of free vortex in compressible flows are simulated by using high precision numerical method to solve for the Navier–Stokes equations. Accurate treatment of the boundary condition is extremely important for simulation of vortex flows. The developed numerical methods are well presented by combining six-order non-dissipation compact schemes with Navier–Stokes characteristic boundary condition having transverse and viscous terms, and can accurately simulate the movement of free vortex. The numerical reflecting waves at the boundaries are well controlled.

An accurate numerical method is developed for computing inviscid flows containing discontinuities. The method is based on flux vector splitting (FVS) and a third-order accurate upwind-biased compact finite-difference scheme. Two different flux splitting techniques, namely, the kinetic flux vector splitting (KFVS) and van Leer's flux splitting, are used to solve one-dimensional gas dynamics test problems. The idea of total variation diminishing (TVD) is employed to suppress spurious numerical oscillations. The stability and high-order accuracy of the scheme are shown.