# Finite difference method

Dear EE Development Team,

I see that EFDC employs the finite difference method (for momentum), so I expect that stability of the model is sensitive to time step. I performed some tests by modeling a simple straight rectangular channel (1-d). At very low flow (very shallow), a stable run can only be performed for a certain time step (the model crashes when increasing or decreasing the time step). I suspect that I may have to reduce the cell size to stabilize the model (flow depth was about 5 cm and Dx=30 cm and Dy = 60 cm). I was trying to test the model for sediment transport simulation with a degradation experiment by Suryanarayana (1969) using a straight flume (18.3 m long, 0.61 m wide, initial bed slope of 0.007 covered by uniform sand D50 = 0.45 mm, Q = 11.9 L/s, initial flow depth 0.034 m). One of my colleagues tested his own model (finite element, 1-d triangular mesh) with this experiment and obtained good results. I ran a similar test for EFDC and it failed. I had to run the model for greater flow to get stable water surface profile (without activating sediment) but when sediment was activated, some instability presented in the channel bed. I guess that refining my mesh sizes would help but I haven’t done that. I would like to hear your comments about this…

The model is finite difference explicit. It is sensitive to the time step but not overly. You can use the CFL calculator in EE to give you some idea of the range of time steps. Depending on how advective the system is the higher you can go. Of course, changing the time step by an order of magnitude up or down could cause problems. Download and use the Yen-Lee U shaped flume test for an example of a flume study of sediment transport. We have extensively tested this and found reasonable results when comparing to the paper. The WEB version of EE does not support sediment transport but you can still run the model and review the hydrodynamics.

EE_Development_Team wrote: The model is finite difference explicit. .

As you said, the model is explicit finite difference, which means we only can choose the explicit numerical scheme to run cases. I found in the manual, there are 3 numerical scheme, one is 3 time level, the second one is explicit, the last one is implicit for 2 time level. but based on my simulation, when choose the implicit scheme, the model seems to have very big numerical viscous, which will lost lots of wave energy. and I also found the source code in the implicit scheme is much less than those in explicit scheme. I tried to find the reason?

Now I understand EFDC model is only explicit scheme!! Thanks.