Hello you all, I am trying to turn our in-house compressible, unstructured, finite volume RANS solver into an LES. The flux discretization is Roe-Upwind 2nd order. The gradient reconstruction exploits least squares. The temporal scheme is a 4th order 6 step Runge-Kutta. I tried to run the solver without turbulent models in an incompressible channel (actually, a DNS), initializing the flow field with a DNS exact solution. Though I am refining the grid up to DNS levels, turbulence dacays very fast with no hope to grow up again. I know it is possible to have LES solvers with Upwind 2nd order, so does anyone have an hypothesis what to check out, or how to behave, or what absolutely to change, or where I am definitely screwing up ? Thanks for your help!

Upwind schemes are highly dissipative and have the potential to wipe out all small scales and laminarize the flow. How about switching to central difference schemes? I remember reading in FLUENT manual too where it is suggested to use central difference schemes for LES solver.

The 2nd order upwind scheme is an unfeasible choice for LES. It has a very bad spectral representation at the highest frequencies, in several aspects the more important ones in an LES.

Due to this bad behaviour, this is probably the cause of the damping of all the fluctuations present in your initial condition. Turbulence is pratically unsustainable on your grid because of the very high artificial dissipation of the scheme.

Some feasible choices are:

1) Switch to a pure 2nd order central scheme and implement some kind of explicit filtering to remove the badly resolved scales from your simulation. Then apply one of the LES turbulence models. A lot of work about the explicit filtering on unstructured grids is available online through the Stanford CTR site.

2) ILES approach. Switch to an higher order central scheme (2nd or higher order) with some kind of limiting. It's nonlinear behaviour will act as a kind of dynamic model.

In the first case you have a formally correct approach and some kind of control over the parameters of your LES, taking numerics, filtering and turbulence modeling as three separate actors in your simulation. Grid convergence is expected for fixed filter size.

In the second case, while having a more simple approach, there are some issues connected with the formulation. Actually, with the classical form of the equations, commutation errors are not properly accounted for and, as a consequence, your solution will not be the filtered one you're looking for. This is important because the commutation error is of the same order of the discretization error so the different error component will interact in a very nonlinear fashion.

This is just to mention some possible solutions. To really implement one of it you should go through the available literature to properly face the several issues connected with both of them.

hope this helps

Thank you for your suggestions, I will try. Do you have any idea on how to increase the order over the 2nd for finite-volumes unstructured grids? Thank you again.

This is actually a very complex task. I'm not very expert in this but some of the issues that need to be faced are:

1) The linear reconstruction method for the variables inside the finite volumes is only second order. You need to switch to, at least, a quadratic reconstruction method. In the former a costant gradient inside the volume is constructed by a least squares method and a linear variation for the variables inside the volume is assumed. In the latter the same method is applied to obtain the Hessian so you can build the quadratic variation inside the volumes. For a clear understanding of this, which i'm actually still missing, you should read the Barth papers on finite volumes

2) The flux computation at faces has to be upgraded with a higher than 2nd one

3) The face integrals of the fluxes has to be computed with accuracy higher than two. You will need the node values which in turn come from interpolation of neighbour cell values. This interpolation has to be of order higher than 2, of course.

4) The geometry described by piecewise linear variations is no more valid. You have to switch, at least, to quadratic piecewise variations.

This is just a taste. Moreover, several approaches are available to face these issues.

To gain more knowledge about these things you can search the following:

High/er order finite volume method

Discontinuous Galerkin method

Spectral volume method

Spectral difference method

A lot of material is freely available online

I suspect you are being limited by the 2nd order FV scheme. It is not impossible to get good solutions using such a scheme, but you will need a lot of grid points. I definitely recommend higher order schemes. Unfortunately, they are difficult to implement in an unstructured code. Discontinuous Galerkin methods are probably the most promising. But, they are an active research topic in themselves right now. If you continue with upwind type schemes, you should read about the MILES approach. There is a book by Grinstein, "Implicit Large Eddy Simulation" that would help.