The simulation of transport phenomena by any numerical method poses the following problem: The convective term in the governing equations generates a broad range of length scales. This range of length scales needs to be accounted for by either:


  1. Modeling: the effect of small scales on coarse scales is modeled and only coarse scales are represented by computational elements (grids, particles).
  2. Resolving: all length scales are resolved by the computational elements.


Using a non-adaptive numerical method leads to a prohibitive computational cost. We have therefore developed a wavelet-based particle method that adaptively represents different length scales.

In the CSElab we have developed a class of dynamically adaptive particle methods by recruiting the compression capabilities of wavelet-based Multiresolution Analyses (MRA).