Contact discontinuity capturing schemes for linear advection and compressible gas dynamics (2002)
| Venue: | J. Sci. Comput |
| Citations: | 12 - 1 self |
BibTeX
@ARTICLE{Després02contactdiscontinuity,
author = {Bruno Després and Frédéric Lagoutière},
title = {Contact discontinuity capturing schemes for linear advection and compressible gas dynamics},
journal = {J. Sci. Comput},
year = {2002},
volume = {16},
pages = {16--479}
}
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Abstract
Abstract We present a non-diffusive and contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to the Ultra-Bee limiter of [20], [24]. We prove for the Ultra-Bee scheme a property of exact advection for a large set of piecewise constant functions. We prove that the numerical error is uniformly bounded in time for such prepared (i.e. piecewise constant) initial data, and state a conjecture of non-diffusion at infinite time based on some local over-compressivity of the scheme for general initial data. We generalize the scheme to compressible gas dynamics and present some numerical results.
