A Positive Finite - Di erence Advection Scheme

1 Abstract. This paper examines a class of explicit nite-diierence advection schemes derived along the method of lines. An important application eld is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity. For the spatial discretization, attention is connned to conservative schemes using 5 points per direction. The 4-th order central scheme and the family of-schemes, comprising the 2-nd order central, the 2-nd order upwind and the 3-rd order upwind biased, are studied. Positivity is enforced through ux limiting. It is concluded that the limited 3-rd order upwind discretization is the best candidate from the four examined. For the time integration attention is connned to a number of explicit Runge-Kutta methods of orders 2 up to 4. With regard to the demand of positivity, these integration methods turn out to behave almost equally and no best method could be identiied.