Freezing similarity solutions in the multi-dimensional Burgers equation

The topic of this paper is similarity solutions occurring in the multi-dimensional Burgers equation and their numerical approximation. We present a simple derivation of symmetries appearing in a family of generalizations of Burgers' equation in d-space dimensions. We use these symmetries to obt...

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Bibliographic Details
Published in:Nonlinearity 2017-11, Vol.30 (12), p.4558-4586
Main Author: Rottmann-Matthes, Jens
Format: Article
Language:English
Subjects:
Burgers' equation
freezing method
meta-stable behavior
relative equilibria
scaling symmetry
similarity solutions
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Summary:The topic of this paper is similarity solutions occurring in the multi-dimensional Burgers equation and their numerical approximation. We present a simple derivation of symmetries appearing in a family of generalizations of Burgers' equation in d-space dimensions. We use these symmetries to obtain an equivalent partial differential algebraic equation (freezing system) that allows us to do direct long-time simulations on a fixed computational domain. As concrete examples, we are able with this method to numerically find similarity solutions for the 2D Burgers equation and observe a metastable behavior of 2D N-wave-like patterns.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa89d5