Two Modified Versions of Bott's Positive-Definite Numerical Advection Scheme

Two modified versions of Bott's forward-in-time, positive-definite numerical advection scheme are described. One version is a conservative flux form; the other is a nonconservative advective form. Both versions demonstrate improved stability in tests involving a strongly deformational flow field. The modified versions are identical to Bott's original scheme for cases of uniform fluid density and purely rotational flow. Additional forms of the odd-order versions of the scheme are presented that exhibit lower phase-speed errors than the original odd-order versions.