Benchmarking a Third-Order Upwinding Scheme

Spurious oscillations in my previous simulations of vortex shedding from rectangles led me to study advection schemes of higher order. My previous code used a modified central differencing scheme which did not adequately predict the fluxes into and out of each cell. These non-physical oscillations around the blunt body are a result of the scheme used. I have implemented a modified Third-Order Upwinding scheme which is flow direction independent as specified by B.P. Leonards paper and similarly implemented in R.W. Davis’ classic paper. The problem using a centered-space scheme, as explained by Leonard, is the order of the truncated terms in the Taylor expansion. Retaining higher-order terms in the Taylor expansion increases spatial accuracy, but requires a larger stencil. This also requires careful implementation near the boundary edges. This does not mean the simulation is third-order accurate since the diffusion and pressure gradient terms are handled using second-order accurate schemes. However flows w