An BD-entropy inequality preserving Finite Volume scheme for the Quantum Navier-Stokes system
Abstract
In this work, we propose a Finite-Volume scheme on cartesian grids for the numerical approximation of some solutions of the Quantum Navier-Stokes Equations. The originality of our contribution is to propose a scheme allowing to provide some discrete BD-entropy inequalities, similarly to the continuous case. To do it, the continuous system is first carefully reformulated. Then, the numerical scheme is based on a time splitting. The hyperbolic step allows to use some classical Finite-Volume schemes, whereas the parabolic step remains linear. Discrete BD-entropy inequalities are established, and numerical tests in 1D and 2D illustrate the efficiency of the scheme in several configurations.
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