LES Method idea
I've been trying to figure out a fast method for LES simulations and I came up with a "demo" concept. As usual in LES, the velocity field is split into high and low frequencies;
u' -> low freq
u'' -> high freq
Where the low freq part is solved and the high freq part is modeled. The high freqs can be modeled either via an SGS model or implicitly using upstream interpolation, but both have their flaws.
SGS model - High computational cost with multiple strain calculations
Implicit - SGS energy dissipation is purely mathematical, i.e. non physical.
To resolve this I came up with the method of using CentralInterp(u') + UpstramInterp(u'') to construct a stable face value. To efficiently but accurately split u' and u'' I thought to use a laplacian smoother as such:
u' = u + k * L(u)
u'' = u - u'
Where k = dx^2 * S / (4 * S + C), S is the local absolute strain rate and C is a constant. This creates a strain based, SGS-model-like, filter with an asymptotic result that converges towards the diffusive CFL limit k = dx^2/4.
This way an Implicit SGS model can be used with a physically true but compuationally friendly filter resulting in a Semi-Implicit Variational Multiscale LES model.
This is currently just a concept, so don't take it too seriously, think of it like a creative excercise/Brainstorm :)
Thoughts?