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Hello,

I'm trying to model a thermal plume in T3D and am looking into the appropriate vertical mixing scheme to use. Perhaps I've overlooked it, but I'm not seeing much documentation on how the turbulent diffusivity of a tracer (in my case temperature) is calculated when using a momentum turbulence closure such as k-epsilon. Am I correct in assuming that the turbulent diffusivity of the tracer is related to the eddy viscosity (provided by k-eps) using a turbulent Prandtl number? If so,

1. What is the keyword for the turbulent Prandtl number and in which Fortran module is it used?

2. Is the Prandtl number always a fixed value or can it depend on stratification in the case of an active scalar?

3. What exactly is the "COEFFICIENT FOR HORIZONTAL/VERTICAL DIFFUSION OF TRACERS"? Is this the molecular or turbulent diffusivity? How does this come into play if the turbulent diffusivity is dynamically calculated?

4. Any suggestions for an appropriate vertical turbulence model for modeling a thermal plume? I'd like to use k-epsilon, but am getting too much vertical mixing.

Thanks in advance,
Ben

Hello,

A few answers to many questions, maybe you can find more in the documentation.

PRANDTL NUMBER is the keyword for the Prandtl number, the default is 1., you can also change it in subroutine CSTKEP.F where you will find a number of others parameters.

With thermal effects and stratifications we favour the k-epsilon model, but too much vertical mixing may not be linked to this model, but rather to the numerical diffusion of advection schemes, and also to the movement of planes in the mesh, which triggers advection in the transformed mesh. You can try to have fixed planes.

The various diffusion coefficients like COEFFICIENT FOR HORIZONTAL/VERTICAL DIFFUSION OF TRACERS are the molecular viscosity if you use k-epsilon (they will be added to the turbulent viscosity).

With best regards,

Jean-Michel Hervouet

Hi Jean-Michel,

Thanks for your quick response! You're right, the k-epsilon model is not the reason for what I'm perceiving as too much mixing. I took your advice an played with different advection schemes on fixed horizontal planes, but didn't notice much difference for my particular test case.

I did notice, however, a HUGE difference when MASS-LUMPING FOR DIFFUSION is set to 1. In this case, my thermal plume remains relatively coherent and propagates through the domain with much less mixing. This is a bit disconcerting for me, because I don't have a good understanding of what MASS-LUMPING entails. I'm assuming it involves restructuring matrices and is purely numerical. Is it correct that turning on mass-lumping for diffusion would have such a big influence on the results? Would you mind explaining a bit what mass-lumping involves and when it is appropriate to invoke?

Cheers,
Ben

Hello,

Sorry to answer late but I am not currently at work. Yes mass-lumping is a purely numerical trick that consists in lumping all terms of a line in a matrix on the diagonal. It is more like finite volumes and may have a smoothing effect. In Telemac it is applied only on the derivative in time (which gives a mass matrix after variational formulation) and should have no effect on steady flows since this derivative cancels. For diffusion it ensures that the result will be monotonous (inverting a mass matrix may create local extrema). If mass-lumping has a large effect in your case it betrays a mesh dependency. Note that mass-lumping a diffusion matrix would just give zero, this is why it is applied only on the mass-matrix.

With best regards,

Jean-Michel Hervouet