Mach reflection for the two-dimensional Burgers equation

M. Brio; J. K. Hunter

doi:10.1016/0167-2789(92)90236-G

Mach reflection for the two-dimensional Burgers equation

M. Brio, J. K. Hunter

Research output: Contribution to journal › Article › peer-review

64 Scopus citations

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.

Original language	English (US)
Pages (from-to)	194-207
Number of pages	14
Journal	Physica D: Nonlinear Phenomena
Volume	60
Issue number	1-4
DOIs	https://doi.org/10.1016/0167-2789(92)90236-G
State	Published - Nov 1 1992

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(92)90236-G

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@article{f826f3028df64efa8a3552c09ac3fd59,

title = "Mach reflection for the two-dimensional Burgers equation",

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.",

author = "M. Brio and Hunter, {J. K.}",

note = "Funding Information: We would like to thank L.F. HendersonE, .G. Puckett and R. Rosales for helpful discussions. We also thank several anonymousre fereesfo r their commentosn earlierv ersionso f this paper. The work of M.B. was partially supportedb y NSF under Grant DMS-8902097A, FOSR under Grant F49620-92-J-0054a,n d by Arizona Center for MathematicaSlc iencess ponsorebdy AFOSR contracFt Q8671-90058w9i th the UniversityR e-search Initiative Program at the Universityo f Arizona. The work of J.K.H. was partiallys up-ported by NSF under Grant DMS-9011548.",

year = "1992",

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doi = "10.1016/0167-2789(92)90236-G",

language = "English (US)",

volume = "60",

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T1 - Mach reflection for the two-dimensional Burgers equation

AU - Brio, M.

AU - Hunter, J. K.

N1 - Funding Information: We would like to thank L.F. HendersonE, .G. Puckett and R. Rosales for helpful discussions. We also thank several anonymousre fereesfo r their commentosn earlierv ersionso f this paper. The work of M.B. was partially supportedb y NSF under Grant DMS-8902097A, FOSR under Grant F49620-92-J-0054a,n d by Arizona Center for MathematicaSlc iencess ponsorebdy AFOSR contracFt Q8671-90058w9i th the UniversityR e-search Initiative Program at the Universityo f Arizona. The work of J.K.H. was partiallys up-ported by NSF under Grant DMS-9011548.

PY - 1992/11/1

Y1 - 1992/11/1

N2 - 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.

AB - 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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U2 - 10.1016/0167-2789(92)90236-G

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-4

ER -

Mach reflection for the two-dimensional Burgers equation

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