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In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving near‐discontinuities and strong streamline curvature. First‐order methods showed significant artificial diffusion, whereas higher‐order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low‐order artificially diffusive schemes, especially in the numerical heat‐transfer industry. This paper presents an alternative strategy of using non‐artificially diffusive higher‐order methods, while maintaining strictly monotonic transitions through the use of simple flux‐limiter constraints. Limited third‐order upwinding is usually found to be the most cost‐effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.
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…
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.