Let us discuss the solution procedure

1. Divide the physical domain by a mesh system where

Figure 24.1

2. Set the known boundary conditions for and

3. Choose initial values of and at the interior grid points. Taking initial values for vorticity as zero is usually acceptable. Initial values for at each column of points can be calculated from the axial velocity profile at that location. However, for interior points may be taken as and

4. Calculate everywhere using equation (24.8). Gauss-Seidel or overrelaxation type calculation is done, for example:

where, is the value from previous calculation, is the most recent value, F is the overrelaxation factor and is newly adjusted better guess.

5. Calculate and at all the internal grid points using equations (24.11 and 24.12).

6. In a subsequent step, calculate at all interior mesh points using equation (24.10).

7. Apply appropriate boundary conditions (which has been discussed, in details, in lecture 25).

8. Go back to step (4) and calculate with the help of current value of and values, where denotes the pervious level. After, evaluating at all points, find out at all points which are indeed improved values. Start repeating steps 4 to 8 untill the desired degree of convergence is achieved.

Congratulations, you have finished Lecture 24. To view the next lecture select it from the left hand side menu of the page or click the next button.