High-order well-balanced finite volume schemes for hydrodynamic equations with nonlocal free energy
Numerical Analysis
2020-11-20 v2 Numerical Analysis
Computational Physics
Fluid Dynamics
Abstract
We propose high-order well-balanced finite-volume schemes for a broad class of hydrodynamic systems with attractive-repulsive interaction forces and linear and nonlinear damping. Our schemes are suitable for free energies containing convolutions of an interaction potential with the density, which are essential for applications such as the Keller-Segel model, more general Euler-Poisson systems, or dynamic-density functional theory. Our schemes are also equipped with a nonnegative-density reconstruction which allows for vacuum regions during the simulation. We provide several prototypical examples from relevant applications highlighting the benefit of our algorithms elucidate also some of our analytical results.
Keywords
Cite
@article{arxiv.2004.05341,
title = {High-order well-balanced finite volume schemes for hydrodynamic equations with nonlocal free energy},
author = {José A. Carrillo and Manuel J. Castro and Serafim Kalliadasis and Sergio P. Perez},
journal= {arXiv preprint arXiv:2004.05341},
year = {2020}
}