open TELEMAC-MASCARET The mathematically superior suite of solvers

Hi all,

I have to explain briefly the principles of the discretization of Time and Space used in Telemac 2d to solve its equations.

I therefore checked the manual whose theme is "The Set of the T2D Equations and their Resolutions" (prin30_gb document).

This thema is there explained from p.56 to 63. It concerns T2D 3.0, but I guess this is clearly for v6.0 still valid.

As far as I understood, and it is more complicated than that, in T2D the Saint-Venant equations are solved most of the time using the method of characteristics, which leads, for the Time, to the fractional step method.

This fractional step method is an implicite finite difference approach of the first order. For some non-linear terms, specialized semi-implicite sub-iterations are prefered.

For Space, the functions are decomposed into bases taking place at each nodes of the irregular mesh of triangular elements. Four-side elements are automatically split into triangles.

Is that ok ? As I said I would just like to sum up the concepts, I cannot restitute the complete elaboration. I would appreciate if someone could confirm/correct me, thank you!

Best Regards,
Jean

Hello,

The method of characteristics is just an option for doing the advection step. It is true however that the solution procedure is split into several fractional steps. You can mention that discretization in space is mostly based on Galerkin finite elements. Discretization in time is closer to finite differences, so a derivative of f with respect to time will be (f(time n+1) - f(time n))/DT. Other variants of finite elements would include the derivative in time in the variational formulation.

With best regards,

Jean-Michel Hervouet