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# ComputerProb4 - Oct 17 2006 ATMS 502 CS 505 CSE 566 Jewett...

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1 Oct. 17, 2006 ATMS 502 - CS 505 - CSE 566 Jewett Computer Problem 4 2D Advection: Rotational and Deformational Flow Due : Tuesday, October 31. Turn in : your code (printed out, and also emailed to me), and plotted results (on paper). Problem being solved: 2-D advection with fractional step (directional) splitting. Boundary condition: 0-gradient (extrapolation outward, whether inflow or outflow) Evaluation: You will compute error statistics for the one case (rotational flow) with a known solution, following Takacs (1985, eqn. 6.1-6.7), evaluated over the 2D domain. Methods: Crowley (Tremback et al., Mon. Wea. Rev. , 1987), 2 nd and 6 th -order. 1. Crowley 2 nd -order (same as Lax-Wendroff) " j n + 1 = " j n + # 2 " j \$ 1 n \$ " j + 1 n ( ) + # 2 2 " j + 1 n \$ 2 " j n + " j \$ 1 n ( ) 2. Crowley 6 th -order See Tremback p. 542, ORD=6 (advective form) For all of the above, " = # t # x local u or v ( ) (i.e. it is the local Courant number) Domain: The computational domain is a two-dimensional staggered C-grid, with the scalar field q stored over a 101x101 domain, with x= y= 1 nx " 1 # \$ % & ( . The physical coordinates for q range from -0.5 to +0.5 in each direction. The

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ComputerProb4 - Oct 17 2006 ATMS 502 CS 505 CSE 566 Jewett...

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