Results

With and without convection

Case 1: Without convection term

The spot goes through the outlet from the shortest path, but its speed is slow

Case 2: With convection term

The spot goes through the outlet from the shortest path and its speed is faster than Case 1.(v = [2, −2, 0])

Controlling the direction

Case 3: Unsuccessful controlling the direction

The outflow velocity overcomes our velocities and changes the path of the spot.

Case 4: Successful controlling the direction

In this case, our velocities can overcome outflow velocity.

Controlling the direction for another spot

Case 5: Unsuccessful controlling the direction

The spot splits and the right part of the spot is trapped while the left part goes left-down through the outlet

Case 6: Unsuccessful controlling the direction

The spot is big and some parts of the spot are also on the right part of the rectangular cube. Hence, the right-hand side of the spot is trapped and the left part goes through the outlet

Case 7: Successful controlling the direction

We change the velocity in the x-direction to 3 and we can overcome the outflow velocity.