Wavelet-Based Local Mesh Adaptation with Application to Gas Dynamics

The paper addresses a simple numerical method for calculating two-dimensional gas dynamics problems on Cartesian meshes with dynamic local refinement. For multilevel local adaptation, several mesh-related algorithms are proposed based on quadric trees and recursive functions. A global analyzer of the computed solution is developed on the wavelet-based decompositions. To project the numerical solution between different mesh levels a procedure is proposed for cell function reconstruction based on the WENO-approach. Different ways of the parallel realization for such dynamic mesh structures are discussed.