Adaptive multiresolution methods applied to hydrodynamics and magnetohydrodynamics

Presented by Margarete Oliveira Domingues

http://www.lac.inpe.br/~margarete/

We present an adaptive finite volume method based on Harten's cell average multiresolution. The space discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge--Kutta scheme for time integration. This multiresolution technique allows to introduce a locally refined spatial mesh while controlling the error. Local time schemes are also discussed. Different applications to hydrodynamical and magnetohidrodynamical problems illustrate the properties of the method. For each application CPU time and memory savings are reported and numerical aspects of the method are discussed. The accuracy of the adaptive computations is assessed by comparison with reference solutions computed on a fine regular mesh or an exact solution.

Join work with: Odim Mendes (DGE/CEA/INPE), Kai Schneider (M2P2--CNRS, Aix-Marseille Université), and the PhD students: Anna Fontes Gomes (CAP/INPE), Muller Moreira Lopes (CAP/INPE)