A Numerical Study of Riemann Problems for the Two-Dimensional Unsteady Transonic Small Disturbance Equation

Abstract

We 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 we present a numerical study of global solution behavior for the values of a and b in a previously obtained bifurcation diagram. Our study supplements the related theoretical results and conjectures recently obtained by S. Canic and B. L. Keyfitz. We employ a high resolution numerical method which reveals fine solution structures. Our findings confirm theoretical results and conjectures about the solution patterns and deepen the understanding of the structure of several intricate wave in...