NON-INVERTED SKEW UPWIND SCHEME FOR THREE-DIMENSIONAL CONVECTIVE TRANSPORT

Abstract

Abstract A non-inverted skew upwind scheme (NISUS), based on a control-volume finite-element formulation for advection-diffusion scalar transport problems, is presented. The formulation is developed with 8-noded hexahedral elements, and an isoparametric interpolation of scalar and geometric variables. The new approach for relating the control-volume surface fluxes of each scalar with the nodal point values is described. Due to the explicit representation in terms of nodal variables, a local inversion of the upwind coefficient matrix is not needed. This feature can reduce the simulation time. The scheme is applied to three of test problems, including convective transport of a step change in a scalar field, combined advection and diffusion in an inlet/outlet tank, and radial heat flow in a rotating hollow sphere. The promising performance of NISUS, as compared with exact and previous methods, is demonstrated in terms of both accuracy and stability. Financial support in the form of a Research Grant from the Natural Sciences and Engineering Research Council of Canada, as well as a Tuition Waiver Award (2002/2003) to E. O. B. Ogedengbe by the University of Manitoba, are gratefully acknowledged.