A numerical study of Riemann problems for the two-dimensional unsteady transonic small disturbance equation

Journal Article · Thu Oct 01 04:00:00 EDT 1998 · SIAM Journal of Applied Mathematics

DOI:https://doi.org/10.1137/S003613999730884X· OSTI ID:653466

Canic, S; Mirkovic, D ^[1]

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1. Iowa State Univ., Ames, IA (United States). Dept. of Mathematics

The authors study a two-parameter family of Riemann problems for the unsteady transonic small disturbance (UTSD) equation, also called the two-dimensional Burgers equation. The two parameters, a and b, which define oblique shock initial data, correspond to the slopes of the initial shock waves in the upper half-plane. For each a and b, the three constant states in the upper half-plane satisfy the Rankine-Hugoniot conditions across the shocks. This leads to a two-parameter family of oblique shock interaction problems. In this paper the authors present a numerical study of global solution behavior for the values of a and b in a previously obtained bifurcation diagram. The study supplements the related theoretical results and conjectures recently obtained by S. Canic and B. L. Keyfitz. They employ a high resolution numerical method which reveals fine solution structures. Their findings confirm theoretical results and conjectures about the solution patterns and deepen the understanding of the structure of several intricate wave interactions arising in this model.

• Sponsoring Organization: National Science Foundation, Washington, DC (United States); USDOE, Washington, DC (United States); Office of Naval Research, Washington, DC (United States)
• DOE Contract Number: FG02-94ER25220
• OSTI ID: 653466
• Journal Information: SIAM Journal of Applied Mathematics, Journal Name: SIAM Journal of Applied Mathematics Journal Issue: 5 Vol. 58; ISSN 0036-1399; ISSN SMJMAP
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
NUMERICAL SOLUTION
RANKINE-HUGONIOT EQUATIONS
SHOCK WAVES
TRANSONIC FLOW
UNSTEADY FLOW