Problem1 - d

Examine the method stability with different grids. Determine the maximum time step that leads to a stable solution and compare it to the stability criteria.

Grid spacing test

Here, the stabilith test is performed with different set of grid spacing. To rule out other effect of numerical setup, Courant number and \(\beta\) remain constant whereas only grid spacing changes. Following table shows the stability check. O denotes the stable condition and X represents the unstable condition.

NxN stability
10x10 X
15x15 X
16x16 X
17x17 O
18x18 O
20x20 O

Maximum time step

In this code, the variable time step method is used to maintain stable numerically. Therefore, the code does not run with constant time step. The maximum time step test is performed with different set of Courant number condition. The grid spacing is fixed with 20x20 to have fast running of simulation.

../../_images/stabilityCr.png
Courant # dt at last iteration
0.5 0.007470
0.51 0.007620
0.55 0.008218
0.6 0.008653
0.8 0.007761