A stable and accurate convective modelling procedure based on quadratic upstream interpolation

A convective modelling procedure which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing, is presented. The algorithm is based on a conservative control-volume formulation with cell wall values of each field written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node. This results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensibility property of upstream-weighted schemes. The consistent treatment of diffusion terms is equivalent to central differencing. An application to a complex unsteady two-dimensional flow is briefly discussed.