Multi‐dimensional monotone flux discretization scheme for convection dominated flows

Deals with the non‐stationary pure convection equation in two dimensions. An attribute of the method is that the advective fluxes are approximated by taking the flow orientations into consideration. The interfacial numerical fluxes are interpolated by virtue of the rational areas which depend on the corner velocity vectors. This leads to a discrete system containing dissipative artifacts in regions normal to the local streamline. Conducts two‐dimensional fundamental studies for the flux discretization developed. These analyses give insight into the order‐of‐accuracy, and the scheme stability. According to the underlying positivity definition, this explicit scheme is, furthermore, classified as conditionally monotonic. This scheme has been applied successfully to solve smooth, sharply varied, and discontinuous transport problems.