mid-term-exam

mid-term-exam - ME 608 Numerical Methods in Heat, Mass, and...

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ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Mid-Term Examination Date: March 9, 2011 6:00 – 8:00 PM Instructor: J. Murthy Open Book, Open Notes Total: 100 points Use the finite volume method in all problems. NAME: Problem Points Score 1 30 2 30 3 40 TOTAL 100 1
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∂φ t + x ( u φ ) = 0 and the stencil of control volumes shown in Fig. 1. Assume u > 0. Figure 1: Computational Domain for Problem 1 (a) Derive the discrete equation corresponding to the implicit central difference scheme. (b) Derive the model equation for the scheme. What is the order of spatial and temporal truncation error? Hint: Be sure that all your derivatives are written at the same time level, and are all located at the same grid point . (c) Using the model equation as a basis, discuss whether the scheme is dispersive or dissipative. (d) Do you need to stabilize the scheme? Justify your answer using the model equation as a basis. 2
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mid-term-exam - ME 608 Numerical Methods in Heat, Mass, and...

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