Parallel Adaptive Wavelet Collocation Method for Solution of Multi-Scale Problems

status: ongoing

Four general classes of methods for solving nonlinear partial differential equations on adaptive computational meshes have been developed by our group. Each method uses the adaptive wavelet collocation method (AWCM) based on bi-orthogonal lifted interpolating wavelets to construct a computational grid adapted to the solution. The wavelet decomposition naturally provides a set of nested multi-scale grids adapted to the solution, and we take advantage of this property in developing our methods.

Compressible Flow around Sphere, Re=1000, Ma=0.7
3D Compressible Flow around Stationary Cylinder, Re=350, M=0.3
Rayleigh-Taylor Instability
Interaction of moving particles with a flow, Re:200-200