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hi everyone


I have a question regarding the keyword "TREATMENT OF THE LINEAR SYSTEM."


I would like to solve the equations of SWE, so that this keyword would take a value of 1. The problem is that it is numerically very unstable. When I change this keyword to 2, adding the keywords "FREE SURFACE GRADIENT COMPATIBILITY" and "MASS-LUMPING ON H" becomes much more stable and I can work well.

My question is, how much error am I adding to my solution, considering this?

Also, I would like if someone could explain to me how the keyword "MASS-LUMPING ON H" works. (I understand that it makes me more stable the solution but I do not understand why)

Thanks

Joaquin

Hello Joaquin

The keyword TREATMENT OF THE LINEAR SYSTEM means that with option 1 you are using the primitive version of the SWE with is a version that uses h, u and v in acoupled way.
Option 2 means that you are using, always the SWE but written like the wave equation. The equations behind is always SWE we change only the way of writing it.
Option two is much more stable and thus recommended for user.

Mass lamping is an other story. It means that in order to alleviate the cost of the resolution of a full linear system, the matrix is "condenseted" in a way that each line is summed and put on the diagonal (for lumping coefficient=1). In that case, matrix becomes diagonal and resolution is straightforward and much cheaper.

You can real much more details about these two points in any good book of linear algebra or on the book of Jean Michel Hervouet.

with my kind regards

Riadh

Hello everyone, about this topic a check the velocities (magnitude) with and without this keyword (TREATMENT OF THE LINEAR SYSTEM), and I realized that the magnitude changes a little bit, so, my result will be changing for the fact that Velocity is eliminated from depth equation (continuity equation) at the discrete level?
And if I change my solver also my velocities change a little bit.
Are changing very much my result using this keyword? Why the water level is not changing?
Thanks in advance.
Best regards

I have forgotten to say that mass lumping plays a major role in the stabilization of the problem since it acts as an additional dissusion. So it stabilizes the flow but increases the numerical diffusion which is a double-edged effect.

Riadh