TY - JOUR
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
DO - 10.1016/0167-2789(92)90236-G
M3 - Article
AN - SCOPUS:33845298703
VL - 60
SP - 194
EP - 207
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-4
ER -