## Contact discontinuity capturing schemes for linear advection and compressible gas dynamics (2002)

Venue: | J. Sci. Comput |

Citations: | 29 - 6 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}

}

### OpenURL

### 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.

### Citations

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Citation Context ...> 1. It is not simple to apply the non-dissipative approach to truly non-linear equations: the reason is the necessity of including some entropy constraints (see for example the approach developed in =-=[17]-=- for Burgers equation). So in the 15sfollowing we would like to introduce a simplified approach. The non-dissipative scheme is applied only to the linearly degenerate part of (24). Let us lay stress o... |

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