Modification of ninth-order weighted essentially nonoscillatory scheme for mixed subsonic/supersonic flow

A study was conducted to demonstrate a modification to the high-order-accurate weighted essentially nonoscillatory (WENO) scheme implementation. The motivation behind this effort was to have a high-order-accurate discretization for the convective fluxes that worked well for subsonic and supersonic flows. A procedure was discussed for constructing high-order-accurate upwind schemes. The researchers suggested reconstructing the flow variables at the left (L) and right side (R) of the i +1/2 interface using high-order-accurate WENO approximations and to employ the Roe scheme. The viscous fluxes were computed using a shifted control volume approach with fourth-order accuracy, and the solution was integrated in time with a second-order-accurate implicit Adams-Moulton scheme. The ghost cell approach was applied at all boundaries to solve the problem in place of one-sided difference stencils and truncated WENO schemes.