- Published 1998

Some techniques for improving the accuracy of multidimensional upwind uctuation distribution schemes for the scalar advection equation are compared. One involves the construction of a consistent Petrov-Galerkin nite element scheme which is equivalent to the uctuation distribution scheme when mass-lumping is applied. Another uses a predictor-corrector technique to improve the approximation. In both cases monotonicity is imposed using a ux-corrected transport approach. A third method is then described which combines the second order accurate Lax-Wendro scheme with the PSI scheme via a uctuation redistribution step which ensures monotonicity (and which is a generalisation of the FCT approach for uctuation distribution schemes). Furthermore, the concept of a distribution point is introduced, leading to a `preferred direction' for the limiting procedure. Extensive numerical results are presented for each of these schemes. 2

@inproceedings{HubbardThe1998MultidimensionalUF,
title={Multidimensional Upwind Fluctuation Distribution Schemes for Scalar Time Dependent Problems},
author={M . E . HubbardThe},
year={1998}
}