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Mach reflection for the two-dimensional Burgers equation |
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| Authors: | M. Brio J.K. Hunter |
| Affiliation: | a Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA b Department of Mathematics and Institute of Theoretical Dynamics, University of California, Davis, CA 95616, USA |
| Abstract: | We study shock reflection for the two 2D Burgers equation. This model equation is an asymptotic limit of the Euler equations, and retains many of the features of the full equations. A von Neumann type analysis shows that the 2D Burgers equation has detachment, sonic, and Crocco points in complete analogy with gas dynamics. Numerical solutions support the detachment/sonic criterion for transition from regular to Mach reflection. There is also strong numerical evidence that the reflected shock in the 2D Burgers Mach reflection forms a smooth wave near the Mach stem, as proposed by Colella and Henderson in their study of the Euler equations. |
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