Re: General questions on grid-based computing
 

I am still not sure I have convinced you that RANS type regridding at every times step on a largely Eulerian grid is unlikely to be a good strategy for LES. Since you seem sold on the idea of regridding, may I suggest you consider a largely Lagrangian approach and track your highly resolved regions. This has various complications such as when to stop faithfully tracking to prevent the grid rolling up, etc... but could probably be implemented within a 100% increase in CPU time. Although popular in early Los Alamos codes and a few shock tracking codes I do not think it is popular these days except for some particle based approaches. Is anyone aware of any such approaches today?

Re: General questions on grid-based computing
 

I am not sold on regridding. However, what would you call meshing a domain that changes at every time-step? Wouldn't it be regridding? Even if you have a fixed number of grid-points and you allow the vertices to change position, it is still (some sort of) regridding. Of course, there is the idea of domain decomposition into blocks, but then there are compatibility constraints at the block interfaces. To the best of my knowledge, the conservativity of most schemes is lost.

Anyway, the question for me is how to best mesh a complex domain in a _physically_ adaptive way. I don't like the idea of using fixed grids - it's a "poor" man's choice.

As for mesh distortion for a Lagrangian approach. You are right, in _grid-based_ mathods, Lagrangian solutions are not a good idea (except for a few cases), and the domain has to be remeshed frequently to correct the situation. However, this is strictly speaking the problem with grid-based methods, because the grids are connected - there is a structure _even_ in unstructured grids. In grid-free methods, the particles are disjoint and there is no connectivity issue. There are other issues here but mesh distortion is not the root cause. I've seen some recent mesh-free finite element (Lagrangian) simulations of a penny dropping into a liquid with severe "mesh" distortion but there were no visible errors in the results!

Adrin Gharakhani