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sample-final-exam-problems

# sample-final-exam-problems - ME 608 Numerical Methods in...

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ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Sample Final Exam Problems April 25, 2006 Instructor: J. Murthy 1. Consider 1-D steady conduction on a uniform mesh of twelve cells, as shown in Fig.1. The domain length is L = 1 . 2 m . Cells 1-4 and 9-12 contain a solid of thermal conductivity k A = 1 W / mK while cells 5-8 contain a solid of thermal conductivity k B = 100 W / mK . There is no source term. The boundary conditions are as shown. A student developing a multigrid procedure decides to use three mesh levels as shown in the figure. (a) Develop the discrete equation set for the three mesh levels using the algebraic multigrid procedure developed in class. (b) Starting with an initial guess of T = 300 K everywhere, perform one V-cycle with ν 1 = 0 (i.e., no Gauss-Seidel sweeps on the down leg) and ν 2 = 1 (i.e., one Gauss-Seidel sweep on the up leg) and show the resulting T solution. 1 2 3 4 5 6 7 8 9 10 11 12 Level 0 Level 1 Level 2 400K 300K Figure 1: Computational Domain for Problem 1 2. Consider steady 2-D conduction in a square domain of side L = 2 m .

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sample-final-exam-problems - ME 608 Numerical Methods in...

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