ON THE COMPUTATIONAL-EFFICIENCY OF CERTAIN UPWINDING SCHEMES

The computational efficiency of certain upwinding schemes for the disc retization of the one-dimensional advection dominated transport equati on are examined. In particular, the first order upwind, the second ord er upwind, the weighted scheme. and the QUICK scheme are considered. T he total computational cost for a prescribed accuracy of these schemes was compared using a general purpose algorithm for the integration of time dependent partial differential equations using the method of lin es. The method of lines approach enables us to utilize the well develo ped methodology for the assessment of computational efficiency of ODE integrators. Moreover, in the time integration, the resulting system o f ODEs is integrated by an efficient variable order/stepsize numerical integration scheme. The results indicate that for small cell Peclet n umber, central differences are superior. For moderate values of the ce ll Peclet number the QUICK scheme is the most attractive. Under high a dvective flow conditions, however, the second order upwinding is the m ost reliable.