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Day22-slides - van Leer Concepts Concepts Atms 502 CS 505...

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1 Atms 502 / CS 505 / CSE 566 Numerical Fluid Dynamics Tue., Nov. 7, 2006 12/6/06 Atms 502 - Fall 2006 - Jewett 2 van Leer: Concepts Concepts : Grid zones Not just point values Local functions describe behavior in zone If look only at zone mean: piecewise constant Next step: piecewise linear This is the mean + a constant slope 12/6/06 Atms 502 - Fall 2006 - Jewett 3 van Leer grid zone averages piecewise constant van Leer: Upstream scheme Familiar… grid point values q n + 1 = q n " c # t # x q i " q i " 1 ( ) = q n " cq i " cq i " 1 [ ] # t # x q 1/ 2 = q 1/ 2 " u q 1/ 2 " u q " 1/ 2 [ ] # t # x 12/6/06 Atms 502 - Fall 2006 - Jewett 4 van Leer (1977) Key concept: integrate under function at time t that will be in zone [0, x] at t+ t . q 1/ 2 = q 1/ 2 dx 0 1 " # $ + q " 1/ 2 dx " 0 $
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2 12/6/06 Atms 502 - Fall 2006 - Jewett 5 van Leer (1977) Fluxes Grid zone boundary velocities (C- grid) shown q 1/ 2 = q 1/ 2 dx 0 1 " # $ + q " 1/ 2
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Day22-slides - van Leer Concepts Concepts Atms 502 CS 505...

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