Hi Aileen,
The reason why you don't see this blow-up in the results is probably because you don't save the results for each simulated time step: the last saved time step in the result file may therefore be far earlier than the blow-up.
A blow-up is related to an instability, and instabilities often occur at places where high velocities occur: so it is often due to velocities more than water depths, and it's hence not surprising that yours is detected at a location with low water depth.
The first thing to check is that you use an appropriate simulation time step. This time step usually needs to be such that the Courant number remains lower than 1. If you're working on flood applications, this results in a time step which is usually lower or equal to the cell size divided by a factor 5. I suggest that you check if this is a case in your model, and reduce the time step if necessary.
If the instability occurs close to a boundary, the problem may also be fixed by smoothing the bathymetry along the boundaries.
I hope these tips can help. Your issue may however be due to something different but it's difficult to give more advices without additional description of the model. So don't hesitate to give more details if that doesn't help.
Best regards,
Mathieu