ComputerProb6 - Dec 6 2006 ATMS 502 CS 505 CSE 566 Jewett...

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ATMS 502 Computer problem 6, page 1 Fall 2006 - Jewett Dec. 6, 2006 ATMS 502 - CS 505 - CSE 566 Jewett Extra Credit: Computer Problem 6 3D nonlinear quasi-compressible flow Due : Wednesday, Dec. 12 Description : This problem is a direct extension of problem 5 to three dimensions. A. Equations There are now five unknowns: two horizontal wind components (u and v), vertical wind (w), potential temperature ( θ ), and pressure (p). The discrete equation form: u: " 2 t u = # u x x u ( ) ( n ) x # v x y u ( ) ( n ) y # w x z u ( ) ( n ) z # 1 $ x % p ( n # 1) + K xx u + yy u + zz u ( ) ( n # 1) v: 2 t v = # u y x v ( ) ( n ) x # v y y v ( ) ( n ) y # w y z v ( ) ( n ) z # 1 y % p ( n # 1) + K xx v + yy v + zz v ( ) ( n # 1) w: 2 t w = # u z x w ( ) ( n ) x # v z y w ( ) ( n ) y # w z z w ( ) ( n ) z # 1 ( ) z z % p ( n # 1) + g # ( ) * + , ( n # 1) z + K xx w + yy w + zz w ( ) ( n # 1) θ : MPL : t # = $ 1 % t F i + 1/2 u , ( ) $ F i $ 1/2 u , ( ) [ ] ( n ) + ( n ) x u [ ] ( n ) $ 1 % t F k + 1/2 w , ( ) $ F k $ 1/2 w , ( ) [ ] ( n ) + ( n ) z w [ ] ( n ) ( ( ) * + + Use strang splitting: F 1 % t /2 ( ) [ ] F 2 % t /2 ( ) [ ] F 3 % t ( ) [ ] F 2 % t /2 ( ) [ ] F 1 % t /2 ( ) [ ] " p : 2 t # p = $ c s 2 % x u ( n + 1) + y v ( n + 1) + z ( ) z w ( n + 1) { } ( ) * + Changes to the key routines in computer problem 5 may be broken down as follows:
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ComputerProb6 - Dec 6 2006 ATMS 502 CS 505 CSE 566 Jewett...

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