High-order well-balanced finite-volume schemes for hydrodynamic equations with nonlocal free energy
File(s)
Accepted version
Author(s)
Carrillo, José A
Castro, Manuel J
Kalliadasis, Serafim
Perez, Sergio P
Type
Journal Article
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 and also elucidate some of our analytical results.
Date Issued
2021-01
Date Acceptance
2020-11-18
Citation
SIAM Journal on Scientific Computing, 2021, 43 (2), pp.A828-A858
ISSN
1064-8275
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Start Page
A828
End Page
A858
Journal / Book Title
SIAM Journal on Scientific Computing
Volume
43
Issue
2
Copyright Statement
© 2021, Society for Industrial and Applied Mathematics
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://epubs.siam.org/doi/10.1137/20M1332645
Grant Number
EP/L020564/1
Subjects
math.NA
math.NA
cs.NA
physics.comp-ph
physics.flu-dyn
65XX (Primary), 35Qxx, 35Q35, 35Q82, 76M12 (Secondary)
Numerical & Computational Mathematics
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0802 Computation Theory and Mathematics
Publication Status
Published
Date Publish Online
2021-03-04