An evaluation of several numerical advection schemes

Abstract Three categories of numerical advection techniques are tested: SHASTA, a flux-corrected onedimensional algorithm; FCT, a multi-dimensional flux-corrected technique; and the BIQUINTIC method, a polynomial approximation algorithm. The tests include the transport of a finite amount of material through a 25 × 25 cell grid driven by three different flow fields: one-dimensional linear flow, two-dimensional linear flow, and rotational flow. For each of these tests, two initial distributions of material are used: a rectangular blockshape and an ellipse-shape. In addition, a test with a non-divergent flow field with a homogeneous material field was performed to check for inherent divergence in a particular method. Results show that the FCT and BIQUINTIC methods maintain the integrity of an initial distribution of material better than SHASTA through a simulation. While SHASTA is the fastest of the methods tested computationally it also produces the greatest amount of spurious numerical diffusion. The FCT method has a tendency to flatten the top of a peaked distribution, and the BIQUINTIC method tends to produce a peak in a top-hat distribution during numerical transport. The BIQUINTIC scheme requires more computer time to execute than the other methods tested.