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# BOUSS-2D Courant Number

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When trying to run my BOUSS-2D model, I run into an error stating that the Courant number must be less than 1.

Has anyone else run into an error like this?

How is the Courant number calculated? I've been searching the ERDC manuals, but no luck on an answer yet.

Thank you.

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SMS computes and displays the Courant number in the BOUSS-2D Model Control Time based on the size of your grid cells and the time step. Reducing your time step will reduce the courant number. There is a good description of courant number on wikipedia:

"For example, if a wave is crossing a discrete grid, then the timestep must be less than the time for the wave to travel adjacent grid points. As a corollary, when the grid point separation is reduced, the upper limit for the time step also decreases. In essence, the numerical domain of dependence must include the analytical domain of dependence in order to assure that the scheme can access the information required to form the solution."

There is also a description in the BOUSS-2D Manual on page 15, and 35

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I've been having trouble even at time step = 1e-9 sec, which seems extraordinarily small.

My grid size is 0.1 m. Could this be too small, as it wouldn't take long to cross a cell?

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That is a very small time step indeed. The smaller your grid cells, the smaller your time step will need to be.

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I've been having trouble even at time step = 1e-9 sec, which seems extraordinarily small.

My grid size is 0.1 m. Could this be too small, as it wouldn't take long to cross a cell?

Forgive me for coming into the chat.

I have used Boussinesq models a lot of times (not yet BOUSS-2D, but perhaps this can be of help).

In my opinion, you should compute the wave length close to your point of interest (you can use dispersion equation or Fenton & McKee, linear theory is enough). After that, a grid size of some L/6 should be your largest choice. Typically, I have used grid sizes of 1 or 2 meters, not more.

Courant number is computed as a function of celerity, grid size and time step as C = v·(Dt/Dx). The Courant Number describes the number of grid points that wave information will travel in one time step

The condition CFL (Courant - Friedrichs - Lewy) is a must to reach convergence. So, as John tells you below, the highest is Dx, the highest is C, and the smallest should be Dt to decrease C.

Hope this helps,

Cheers,

Jose

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