Title: Numerical simulations of transonic flows with non-unique solutions

Authors: A.M. Chuen; M. Hafez

Addresses: Department of Mechanical and Aerospace Engineering, University of California, Davis, California, USA ' Department of Mechanical and Aerospace Engineering, University of California, Davis, California, USA

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.

Keywords: transonic flows; Euler equations; isentropic Euler equations; numerical schemes; non-unique solutions; overflow code.

DOI: 10.1504/IJAD.2021.112747

International Journal of Aerodynamics, 2021 Vol.7 No.2, pp.127 - 150

Published online: 01 Feb 2021 *

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