MULTIDIMENSIONAL SINGLE-STEP VECTOR UPWIND SCHEMES FOR HIGHLY CONVECTIVE-TRANSPORT PROBLEMS

After a synthesis of existing numerical approaches, a family of single -step time-marching upwind schemes is proposed for the convective-diff usive balance of a scalar in multidimensional incompressible laminar f lows. A functional description of the new approach is given too. The s chemes are adequate to the simulation of purely or highly convective t ransport phenomena. The proposed schemes were applied to a scalar test problem (rotating hill) and the results evaluated after an analysis o f the intrinsic limitations of test itself. A third-order, fully upwin d-biased scheme of the family is applied to the lid-driven and thermal ly driven square cavity problems. In the lid-driven case a steady-stat e solution is not achieved at Re = 10(4).