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lec21_10302006

# lec21_10302006 - 10.34 Numerical Methods Applied to...

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10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #21: TA Tutorial on BVPs, FEMLAB®. BVPs What methods to use for each situation: 1D o Finite Differences o ODE’s x x 2 nd order: Î Two 1 st order 1 st order: Æ Shooting 2D Rxn fast portion of reaction with adaptive time stepping Capture the fast o Finite Differences Figure 1. Boundary layer. o Method of Lines Stiff o Non-uniform grid 3D o Finite Element o Finite Volume Generally use commercial code Figure 2. Adaptive time stepping. Coding Boundary Conditions Linear: A ·x = b = 0 state variables at grid points BC: x 1,j = 1 Δ x dx d j j j j 2 4 3 , 3 , 2 , 1 , 1 θ θ θ θ 1 for 0 , 1 = j dx d θ % % % % % % % 0 % % % % % % % % % % % % % % % % % % % % % % % % 0 0 0 y x N N j i x x x , , 1 , 1 # =

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lec21_10302006 - 10.34 Numerical Methods Applied to...

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