Multiresolution schemes for conservation laws

In recent years a variety of high-order schemes for the numerical solution of conservation laws has been developed. In general, these numerical method s involve expensive flux evaluations in order to resolve discontinuities ac curately. But in large parts of the flow domain the solution is smooth. Hen ce in these regions an unexpensive finite difference scheme suffices. In or der to reduce the number of expensive flux evaluations we employ a multires olution strategy which is similar in spirit to an approach that has been pr oposed by A. Harten several years ago. Concrete ingredients of this methodo logy have been described so far essentially for problems in a single space dimension. In order to realize such concepts for problems with several spat ial dimensions and boundary fitted meshes essential deviations from previou s investigations appear to be necessary though. This concerns handling the more complex interrelations of fluxes across cell interfaces, the derivatio n of appropriate evolution equations for multiscale representations of cell averages, stability and convergence, quantifying the compression effects b y suitable adapted multiscale transformations and last but not least laying grounds for ultimately avoiding the storage of data corresponding to a ful l global mesh for the highest level of resolution. The objective of this pa per is to develop such ingredients for any spatial dimension and block stru ctured meshes obtained as parametric images of Cartesian grids. We conclude with some numerical results for the two-dimensional Euler equations modeli ng hypersonic flow around a blunt body.