A Barely Implicit Correction for Flux-Corrected Transport.

The Barely Implicit Correction, or BIC, is a technique to remove the stringent limit on the timestop imposed by the sound speed in explicit methods. This is done by adding one elliptic equation which has to be solved implicitly. BIC is combined with the Flux-Corrected Transport FCT algorithm in order to represent sharp gradients in subsonic flows accurately. The resultant algorithm costs about the same per timestep as a single explicit timestep calculated using an optimized FCT module. Several examples show the techniques ability to solve nearly incompressible flows very economically. The major gain is that the timestep is no longer restricted by the sound speed. This improvement is achieved at little or no additional cost per timestep. The cost of solving the elliptic equation is recovered by the elimination of the half-step calculations in explicit FCT. In two-dimensional problems, an efficient method of solution of the elliptic pressure equation is essential. The multigrid technique MGRID used here is among the fastes. However, the application of this technique to even modestly complicated geometries is not straightforward. Unstructured multigrid methods should provide the necessary flexibility.