Testing 2D Area Grid Cell Size

[Scott Miller]

I’m running a full 2D model with a couple of internal 2D area connections, testing grid cell sizes at 96, 72, 48, and 24 feet general cells sizes. Break lines are holding a stream alignment at 24 foot cell sizes. Courant condition is controlling the time step.

From a base time step of 4 seconds, the Courant number did not change the time step. The volume error for 96 and 72 foot grids was on the order of 0.005%. The volume error for 48 and 28 foot grids was higher, on the order of 0.1%.

Looking just at the maximum flood WSE across a break line, the larger cell grids have less difference in elevation – 0.01 and 0.02 foot, comparing adjacent cells. The smaller cell grids maximum elevations diverge by greater amounts from the 96 foot grid – 0.03 foot for the 48, and 0.06 for the 24.

The smaller the grid cells, the larger the difference between maximum elevations.

Now I’m running the meshes at a 2 second base time step, and the Courant number is not changing the time step. Full momentum, theta = 0.6, Courant number between 0.45 and 1.0 (for all cases). So far the volume errors are much smaller, and the maximum WSEs at the break line are identical to respective model runs at the 4 second time step. No change.

Are the smaller mesh cell sizes supposed to yield the same results for otherwise identical geometries? I thought I understood that I had to drill the size down until there was no computational difference, but it does not seem to be going that way.

[Jarvus]

Making the cells smaller until they no longer change the results is sort of a rule of thumb, but I don’t think it is an absolute.

This model is 2D cells only? No lateral structures, 2D connectors factoring in?

Another possibility to think about: as your cells get smaller and the time step gets smaller, you may need to make the convergence tolerances tighter. If you are getting an error of 0.01′ every second (and the errors are accumulating as opposed to more or less canceling out), that could be a bigger deal than getting an error of 0.01′ for a thirty second time step. Just something I’m throwing out. Can’t say I’m speaking from detailed experience on this.

[Scott Miller]

Thank you, Jarvus. These geometries are all 2D, with internal connections.

I’ve run the 96, 72, and 48 foot meshes at both 4 seconds and 2 seconds, and each mesh gets the same results regardless of the time step. The volume error is clearly smaller with the smaller time step – same results.

As it turns out I put Courant criteria in a plan without checking the box. At a glance the Courant numbers range from 0.01 to 0.35, well below the criteria.

I think the model is solid enough I can go forward with it, and that minute differences in results are artifacts of the mesh alignments on terrain. Calibration would have more bearing on the results than mesh artifacts.

[cameron]

One thing you also always want to check is how the results compare to the diffusion wave solver and a 1D calculation.

I have noticed a few times that the full momentum solver water surface results seem to go up when I go to smaller cells and some times give unrealistic answers (feet higher) when checked against larger grid cells, 1D results, or the diffusion wave solver.

[Scott Miller]

Good point. Thank you, Cameron!

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