New Extended Formulations of Euler-Korteweg Equations Based on a Generalization of the Quantum Bohm Identity

TL;DR

This paper introduces a novel extended formulation of Euler-Korteweg equations using a generalized quantum Bohm identity, enabling entropy-stable numerical schemes and discussing applications to Navier-Stokes equations with degenerate viscosities.

Contribution

It presents a new extended formulation of Euler-Korteweg systems based on a generalized quantum Bohm identity, facilitating entropy-stable numerical methods.

Findings

Enables construction of entropy-stable numerical schemes under hyperbolic CFL condition.

Provides insights into applying the identity to Navier-Stokes equations with degenerate viscosities.

Introduces a generalized quantum Bohm potential identity for extended formulations.

Abstract

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.