Abstract: "This paper examines a class of explicit finite- difference advection schemes derived along the method of lines. An important problem field is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity and on the use of locally refined grids. For the sp...

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Format:	Buch
Sprache:	English
Veröffentlicht:	Amsterdam 1993
Schriftenreihe:	Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1993,9
Schlagworte:	Finite differences
Zusammenfassung:	Abstract: "This paper examines a class of explicit finite- difference advection schemes derived along the method of lines. An important problem field is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity and on the use of locally refined grids. For the spatial discretization, attention is confined to directionally-split schemes in conservation form using 5 points per direction. The 4-th order central scheme and the family of [kappa]-schemes comprising the 2-nd order central, the 2-nd order upwind and the 3-rd order upwind biased discretization are studied. Positivity is enforced through flux 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 confined 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 identified. For solutions with steep gradients, a local uniform grid refinement technique is proposed as an effective tool to speed up computations.
Beschreibung:	28 S.