me180_hw06

# me180_hw06 - HOMEWORK 6 TIME DEPENDENT PROBLEMS IN 1-D...

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HOMEWORK 6: TIME DEPENDENT PROBLEMS IN 1-D TRANSIENT REACTION-DIFFUSION Derive the weak form of the boundary value problem shown below for a backward (implicit) Euler scheme. Solve the following boundary value problem ( L = 1) in COMSOL ˙ c = d dx p D dc dx P - τc D ( x ) = 10 DIFFERENT SEGMENTS ( SEE BELOW ) τ ( x ) = 10 DIFFERENT SEGMENTS ( SEE BELOW ) c ( x = 0 ,t ) = 0 . 5 D dc dx ( x = L,t ) = 5 × 10 - 6 c ( x,t = 0) = 0 . 5 0 < x < L (1) with 100 elements ( δx = 0 . 01) and set the total amount of time to be T = 100 × ( δx ) 2 D ave . Use the backward (implicit) Euler time integration scheme. (Hint: This is a BDF method of order 1) Solve with the following time step sizes: (I) δt = T 100 , (II) δt = T 1000 and (III) δt = T 10000 with FOR 0 . 0 < x < 0 . 1 D = 2 . 5 × 10 - 6 FOR 0 . 1 < x < 0 . 2 D = 1 . 9 × 10 - 6 FOR 0 . 2 < x < 0 . 3 D = 1 . 25 × 10 - 6 FOR 0 . 3 < x < 0 . 4 D = 0 . 15 × 10 - 6 FOR 0 . 4 < x < 0 . 5 D = 1 . 55 × 10 - 6 FOR 0 . 5 < x < 0 . 6 D = 2 . 25

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## This note was uploaded on 08/01/2008 for the course ME 180 taught by Professor Zohdi during the Spring '08 term at Berkeley.

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me180_hw06 - HOMEWORK 6 TIME DEPENDENT PROBLEMS IN 1-D...

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