A minimum entropy principle in the compressible multicomponent Euler equations

¹ Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA
² NASA Advanced Supercomputing Division, NASA Ames Research Center, Moffett field, CA, USA
³ Department of Mathematics, Institute for Physical Sciences & Technology (IPST) and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, USA

^* Corresponding author: gouasmia@umich.edu

Received: 20 June 2019
Accepted: 19 September 2019

Abstract

In this work, the space of admissible entropy functions for the compressible multicomponent Euler equations is explored, following up on Harten (J. Comput. Phys. 49 (1983) 151–164). This effort allows us to prove a minimum entropy principle on entropy solutions, whether smooth or discrete, in the same way it was originally demonstrated for the compressible Euler equations by Tadmor (Appl. Numer. Math. 49 (1986) 211–219).