Diffusion and dispersion errors of the Phoenical Upwind method

The inviscid form of Burger's equation is solved numerically using the Phoenical Upwind method. A nonlinear Hirt stability analysis is carried out. It is shown that the flux limiting process is responsible for modifying the advection speed in the shock region to reduce the dispersion errors. The linear and the nonlinear diffusion coefficients are of the same sign, i.e., diffusion errors are dominant. The flux limiter preserves the conservation property.