BOTTS AREA-PRESERVING FLUX-FORM ADVECTION ALGORITHM - EXTENSION TO HIGHER ORDERS AND ADDITIONAL TESTS

Bott's forward-in-time, positive-definite, area-preserving flux-form a dvection algorithm is extended to higher orders. The new algorithm ver sions are tested with two-dimensional flow fields: a purely rotational how and a purely deformational flow. The results suggest that a balan ce between required accuracy and reasonable computational cost is obta ined for schemes with orders of 3-6, with distinction to the fifth-ord er algorithm. It is also shown that modified odd-order schemes success fully avoid significant phase-speed errors and furnish results that ar e very close to that obtained with the next-higher even-order scheme b ut with a lower computational cost.