Provably positivity-preserving semi-implicit HTC scheme

Develop a provably positivity-preserving variant of the semi-implicit hyperbolic and thermodynamically compatible scheme for the compressible Euler equations that guarantees positivity of density and pressure despite the use of the global Abgrall-type energy correction.

Background

The paper introduces a semi-implicit thermodynamically compatible finite-volume scheme for the compressible Euler equations that evolves entropy as a primary variable, treats acoustic terms implicitly, and enforces total-energy conservation through a global Abgrall-type correction. The correction is designed to achieve global energy conservation to machine precision, but its effect on the admissibility constraints of the Euler equations is not controlled by construction.

In particular, physical admissibility requires the density and pressure to remain positive. The authors explicitly identify the construction of a variant with a provable positivity-preservation property as unresolved future work. Establishing such a variant would strengthen the scheme's reliability for demanding compressible-flow simulations and would support its extension to more complex systems, including multiphase flows and magnetohydrodynamics.