Consider developing adaptive grid techniques for flamelets
Consider using an adaptive grid technique to avoid arbitrary clustering or large uniform grids. This is targeting 'tricky' flamelets like those with complicated, hot fuel streams as in coal simulation. In these systems it is essentially impossible to use the same clustered grid for all parameter space (e.g. dissipation rate, convection coefficient, fuel stream composition), which means we have to use a bigger grid to resolve gradients/curvature (important for robustness of the solver). An adaptive grid technique could be an excellent solution to problems like this.
The attached files (put them all in a folder, run solvingflamelets.py
for a flamelet example, initialgo.py
for a simple function-based adaptation demo) use a simple heuristic that adapts a grid based on local curvature (not including the slope). This is slow because I do a full solve at each refinement/coarsening level, and because it's my first attempt. It can likely be made far faster. It also, in my opinion, over-resolves things and is extremely sensitive to the adaptation tolerance. And it should do adaptivity based on both the gradient and curvature (the function-based demo does this).