New Extended Formulations of Euler-Korteweg Equations Based on a Generalization of the Quantum Bohm Identity
This work provides a novel mathematical formulation for Euler-Korteweg systems, offering a pathway to stable numerical schemes, which is relevant for researchers in computational fluid dynamics and mathematical physics.
The paper proposes a new extended formulation of Euler-Korteweg equations using a generalized quantum Bohm identity, enabling a numerical scheme with entropy stability under a hyperbolic CFL condition. The approach is also applied to compressible Navier-Stokes equations with degenerate viscosities.
In this note, we propose an original extended formulation of Euler-Korteweg systems based on a generalization of the quantum Bohm potential identity. This new formulation allows to propose a useful construction of a numerical scheme with entropy stability property under a hyperbolic CFL condition. We also comment the use of the identity for compressible Navier-Stokes equations with degenerate viscosities.