Finding solutions of the multi-dimensional compressible Euler equations

Organized by: FAU DCN-AvH, Chair in Applied Analysis – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)
Speaker: Prof. Dr. Christian Klingenberg
Affiliation: Universität Würzburg (Germany)

Zoom link
Meeting ID: 998 6927 2903 | PIN code: 072804

Abstract. This talk will survey some results for the two- or three-space dimensional compressible Euler equations, results both in theory and numerics. We shall present
• non-uniqueness results of weak entropy solutions for special initial data using convex integration
• introduce solution concepts beyond weak solutions that allows to show convergence to the incompressible limit of the compressible Euler equations with gravity
• the relationship between stationary preservation, maintaining vorticity, and asymptotic preserving numerical methods
• introduce a high order numerical method that holds promise to achieve this.
This is joint work among others with Simon Markfelder, Wasilij Barsukow, Eduard Feireisl and Phil Roe.

References
[1] W. Barsukow, J. Hohm, C. Klingenberg, and P. L. Roe. The active flux scheme on Cartesian grids and its low Mach number limit. Journal of Scientific Computing 81, pp. 594–622 (2019)
[2] E. Feireisl, C. Klingenberg, O. Kreml, and S. Markfelder. On oscillatory solutions to the complete Euler equations. Journal of Differential Equations 296 (2), pp. 1521-1543 (2020)