Abstract
Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for compressible fluid flow. The extension of the multiresolution-based mesh adaptation concept to high-order discontinuous Galerkin discretization can be performed using multiwavelets, which allow for higher-order vanishing moments, while maintaining local support. An implementation for scalar one-dimensional conservation laws has already been developed and tested. In the present paper we extend this strategy to systems of equations, in particular to the equations governing inviscid compressible flow.
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Financial support from the Deutsche Forschungsgemeinschaft (German Research Association) through grant GSC 111 and in the frameworks of the Collaborative Research Center SFB-TR-40 and the Research Unit FOR 1779, and by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under Grant number FA8655-08-1-3060, is gratefully acknowledged.
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Gerhard, N., Iacono, F., May, G. et al. A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows. J Sci Comput 62, 25–52 (2015). https://doi.org/10.1007/s10915-014-9846-9
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DOI: https://doi.org/10.1007/s10915-014-9846-9