Bott’s Area-Preserving Flux-Form Advection Algorithm: Extension to Higher Orders and Additional Tests

Bott’s forward-in-time, positive-definite, area-preserving flux-form advection algorithm is extended to higher orders. The new algorithm versions are tested with two-dimensional flow fields: a purely rotational flow and a purely deformational flow. The results suggest that a balance between required accuracy and reasonable computational cost is obtained for schemes with orders of 3–6, with distinction to the fifth-order algorithm. It is also shown that modified odd-order schemes successfully avoid significant phase-speed errors and furnish results that are very close to that obtained with the next-higher even-order scheme but with a lower computational cost.