238 RWTH Publication No: 47193        2004        IGPM238.pdf
TITLE Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
AUTHORS Siegfried Müller, Youssef Stiriba
ABSTRACT In recent years the concept of fully adaptive multiscale finite volume schemes for conservation laws has been developed and analytically investigated. Here the grid adaptation is performed by means of a multiscale analysis based on biorthogonal wavelets. So far, all cells are evolved in time using the same time step size. In the present work this concept is extended incorporating locally varying time stepping. A general strategy is presented for explicit as well as implicit time discretization. It can be applied to a scalar equation and systems of equations for arbitrary space dimensions. For reasons of simplicity, the strategy is developed in detail for one-dimensional problems. The efficiency and the accuracy of the proposed concept is numerically investigated for 1D scalar conservation laws. First 2D Euler computations verify that it can also be applied to multidimensional systems.
KEYWORDS multiscale techniques, local grid refinement, locally varying time stepping, finite volume schemes, conservation laws
DOI 10.1007/s10915-006-9102-z
PUBLICATION Journal of scientific computing
30(3), 493-531 (2007)