ME 608
Numerical Methods in Heat, Mass, and Momentum Transfer
MidTerm 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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 Fall '10
 NA
 Numerical Analysis, Umax, discrete equation

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