284 RWTH Publication No: 47085        2008        IGPM284.pdf
TITLE On the Stability of Fully Adaptive Multiscale Schemes for Conservation Laws Using Approximate Flux and Source Reconstruction Strategies
AUTHORS Nune Hovhannisyan, Siegfried Müller
ABSTRACT In order to accelerate finite volume schemes applied to (inhomogeneous) hyperbolic conservation laws multiresolution based adaptive concepts can be used. The basic idea is to analyze the local regularity by means of a multiresolution analysis of cell averages. By difference information between successive refinement levels local grid adaptation is triggered employing threshold techniques. This leads to a significant gain in computational complexity. The crux is to compute numerical and sources on local resolution levels such that the overall accuracy of the reference solution on the finest discretization is maintained. In the present work a modified approach based on polynomial reconstruction techniques is introduced and investigated analytically. The efficiency and accuracy of the adaptive concept is significantly improved, in particular for inhomogeneous equations. This is confirmed by numerical parameter studies.
KEYWORDS conservation laws, finite volume schemes, grid adaption, biorthogonal wavelets
DOI 10.1093/imanum/drp010
PUBLICATION IMA journal of numerical analysis
IMAJNA 30(4), 1256-1295 (2010)