Advection Tests of Optimal Compact Implicit Scheme

Gross, Koseff, and Monismith used two advection test cases to expose the poor performance of seven widely used explicit numerical schemes. Here, those test cases are used to reveal the weakness and strength of the optimal compact implicit scheme. In the diagonal advection of a sharp square block, there are sawtooth grid scale errors. Binomial smoothing, with standard deviation of one grid spacing of the initial square block is required before the optimal compact implicit scheme improves upon the best of the explicit schemes. For the circular advection of a smooth narrow Gaussian cone, the accuracy is 105 times better than the best of the explicit schemes.