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Numerical modeling of a time-fractional Burgers equation

Lombard, Bruno and Matignon, Denis Numerical modeling of a time-fractional Burgers equation. (2017) In: 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2017), 15 May 2017 - 19 May 2017 (Minneapolis, United States).

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Official URL: https://ccaps.umn.edu/documents/CPE-Conferences/WAVES2017BookofAbstracts.pdf

Abstract

A fractional time derivative is introduced into Burgers equation to model losses of nonlinear waves arising in acoustics. A diffusive representation of the fractional derivative replaces the non-local operator by a continuum of memory variables that satisfy local ordinary differential equations. A quadrature formula yields a system of local partial differential equations. The quadrature coefficients are computed by optimization with a positivity constraint. One resolves the hyperbolic part by a shock-capturing scheme, and the diffusive part exactly. Extensive details can be found in [3].

Item Type:Conference or Workshop Item (Paper)
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Other partners > Aix-Marseille Université - AMU (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Ecole Centrale Marseille (FRANCE)
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Deposited By: Denis Matignon
Deposited On:13 Jun 2018 10:45

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