Small Grid Testing of Finite Difference Transport Schemes

Abstract

The following finite difference schemes are employed in an alternating direction-implicit format to approximate the linear form of the two-dimensional constituent transport equation: (1) Forward time centered space (FTCS); (2) forward time upwind space (FTUS); (3) spread time centered space (STCS); (4) spread time upwind space (STUS); and (5) flux-corrected transport (FCT). Several test problems for which analytical solutions are available are considered on a small (7 × 8) uniformly spaced computational grid. It is shown that the FCT scheme exhibits superior numerical properties. Additional tests on a (60 × 60) uniformly spaced grid confirm the small grid tests. Although all the small grid tests were performed on a Cray-I supercomputer, it is demonstrated that these tests may be duplicated on currently available mini- and microcomputers. Therefore, the engineer may screen new finite difference transport schemes on local mini- and microcomputers prior to incorporating these schemes in large grid prototype supercomputer simulations.