Numerical simulations of transonic flows with non-unique solutions

Abstract

Inviscid, compressible flows are described by a first-order system of hyperbolic partial differential equations in conservation form, and are solved numerically with simple schemes. These schemes show the ability to reproduce well-known solutions and benchmarks for the two-dimensional Euler equations. Finally, the schemes are used to explore the anomaly of non-unique solutions in the transonic regime. Furthermore, numerical solutions for the isentropic Euler equations with γ = 2, which are analogous to the shallow water equations, also exhibit non-uniqueness. In the appendix, results computed with OVERFLOW also exhibit non-unique solutions for the same geometries considered in the text.