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Hello,

I study breaching of embankment by overtopping and I try to define the parameters useful of my model (before complicate it with erosion). I joined my file with my parameters. I tested the inflence of several parameters : SUPG Option, solver accuracy, mass-lumping, implicitation, depth in friction terms, type of advection, free surface gradient compatibility, friction coefficient, to find the best configuration (to stabilize the calculation).

Now, I test the velocity diffusivity and I have a problem: I tried a coefficient of 0.005, 0.05, 0.01, 0.5 and 1 and I observed velocities in a same point (I joined my results). For lower coefficients, there are fluctuations at the beginning of overtopping. And for high coefficients, this fluctuations disappear but new appear later. I don't understand this effect. And I don't know what can I do to have a steady calculation.

(My goal is to choose a coefficient realistic, because I will study erosion later and this coefficient impact velocity, so shearing stress, so erosion.)

Thank you!

Hello,

It depends on your mesh size, maybe a value of 1 is too high (compare to U*DX/2 for example, which gives an idea of the numerical diffusion). ANother solution would consist of looking at what value is given by the k-epsilon model.

Regards,

Jean-Michel Hervouet

Thank you.

So, with the k-epsilon model, I could know velocity diffusivity? But, in this model, I have to fix this coefficient 10-6, haven't I? It's eddy viscosity which change?

Hello,

This fluctuations can be observed for regions with tidal flat efects. I guess that your point I is located at the top of the dyke. In that case, many parameters can influence the behaving of the velocity field (mesh discretization, the shape of the dyke (is it as a chineese hat or not), receding, friction ceofficient, etc...)
Actually, with big diffusivity coefficients, the solution will be more diffuse and may generate small water depthes in the limits of wetted areas which will amplify tidal flat effects.

I hope that this helps

Riadh ATA

Thank you.

Actually, my point is on the downstream face of the embankement (after the overtopping). The shape of the dyke is as a chineese hat. I have a friction coefficient of 25 (and I don't want to change this coefficient).

What is the link between velocity diffusivity and numerical diffusion? Velocity diffusivity have to be lower than coefficient of numercial diffusion (=U*DX/2, in 1D)? (I observed that when it's not the case, there are fluctuations)

Ok, I tried the k-epsilon model. I found a value of viscosity of 0.004 when the calculation is stable (I join my graph). But, I don't know how I can interpet that, if I have to fix a velocity diffusivity of 0.004 when I choose the model with constant viscosity? Because there will still have fluctuation (I already tested 0.005 and 0.05, same results). And if I look the viscosity when there are fluctuations, it's worse (because lower).

And, if I understand, the artificial diffusion was introduced by the choice of the SUPG option. I chose a upwind coefficient equal to Courant number because my calculation was more stable, there were fewer flucutations, but not at the beginning. So, the introduction of this artificial diffusion improve my calculation but create a new problem...isn't it?

Hello
The velocity diffusivity is a parameter that you introduce in order to be used as a weight for the diffusion part of calculation, i.e. it is the coefficient you will find linked to the Laplacian operator. In the other side, numerical diffusion is an "uncontrolled" diffusion that is automatically introduced in the calculation and which is due to several reasons (mesh more/less coarse, numercial schemes more/less diffusive etc...) It can be estimated by U*DX/2 for the 1D case. For 2D and 3D cases, this formula gives just an order of magnitude.

Yes and No: the SUPG is a way to change (upwind) the test function in the finite element variational formulation in order to avoid spurious oscillations and in some way to verify the inf-sup condition. Yes, SUPG introduces numerical diffusion but it does it like all other advection schemes. The use of other options will introduce more or less numerical diffusion. An upwind using the Courant number is more recommended.

I hope that this helps

With my best regards

Riadh ATA