Numerical Study of Non-uniqueness for 2D Compressible Isentropic Euler Equations

Abstract

In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin. These are different from the multi-dimensional Riemann problems widely studied in the literature. Our computations provide numerical evidence of the existence of initial value problems with multiple solutions, thus revealing a fundamental obstruction toward the well-posedness of the governing equations. The compressible Euler equations are solved using the positivity-preserving discontinuous Galerkin method.

16 pages, 26 figures; accepted manuscript

References in corpus (2)

• Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations
• On the convergence of the spectral viscosity method for the two-dimensional incompressible Euler equations with rough initial data