A POSITIVE FINITE-DIFFERENCE ADVECTION SCHEME

This paper examines a class of explicit finite-difference advection sc hemes derived along the method of lines. An important application fiel d is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity. Far the spatial discretization, attention i s confined to conservative schemes using five points per direction, Th e fourth-order central scheme and the family of K-schemes, comprising the second-order central, the second-order upwind, and the third-order upwind biased, are studied. Positivity is enforced through flux limit ing. It is concluded that the limited third-order upwind discretizatio n is the best candidate from the four examined, For the time integrati on attention is confined to a number of explicit Runge-Kutta methods o f orders two up to four. With regard to the demand of positivity, thes e integration methods turn out to behave almost equally and no best me thod could be identified. (C) 1995 Academic, Press, Inc.