EML 5725 Computational Fluid Dynamics 4/2/03
Closed book Van Dommelen 10:45-11:35 pm

1.

The MAC scheme uses staggered locations of the velocity components u and v as shown below. Thus the continuity equation can be approximated to second order using the following simple formula:

Here j is the mesh line index in the horizontal direction and l the one in the vertical direction. Determine whether this formula is conservative.

Solution

2.

Consider the nonuniform mesh shown below, where j is the mesh line index in the horizontal direction and l the one in the vertical direction. The mesh spacings are, by definition, and . Derive a second order accurate formula for the derivative at an arbitrary wall point j,0 using the values of the temperature T_j,0, T_j,1, and T_j,2 and the mesh spacings. Show the second order accuracy.

Solution

3.

Determine the stability of the following scheme:

Solution