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Unformatted text preview: ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Final Examination Date: May 4, 2011 1:00 3:00 PM Instructor: J. Murthy Open Book, Open Notes Total: 100 points Use the finite volume method in all problems. NAME: Problem Points Score 1 50 2 50 TOTAL 100 1 1. Consider steady convection and diffusion of a scalar in a square domain, as shown in Fig. 1. The governing equation is given by: ( V ) = ( )+( 1- ) The left and bottom boundaries are at = 0 and = 1 respectively, while the other two boundaries are outflow boundaries. The flow field is given by V = i + j . The density = 1 and = 1 . 0. The side of the square is given by L = 2. (a) Derive the discrete algebraic equations for for the four cell centroids shown at the finest mesh level in Fig. 1. Use a first-order upwind difference scheme for the convective operator. (b) Now derive the discrete algebraic equations for the corrections for the coarse levels 1 and 2 in Fig. 1 using the(b) Now derive the discrete algebraic equations for the corrections for the coarse levels 1 and 2 in Fig....
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