2020/04/11 by José A. Carrillo, Carrillo, José A., Manuel J. Castro +5 · 1 citation
Engineering · Mathematics · #35Q35 #35Q82 #35Qxx #65XX (Primary) #76M12 (Secondary) #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Lattice Boltzmann Simulation Studies #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2004.05341
openalex publication_date 2020/04/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We propose high-order well-balanced finite-volume schemes for a broad class\nof hydrodynamic systems with attractive-repulsive interaction forces and linear\nand nonlinear damping. Our schemes are suitable for free energies containing\nconvolutions of an interaction potential with the density, which are essential\nfor applications such as the Keller-Segel model, more general Euler-Poisson\nsystems, or dynamic-density functional theory. Our schemes are also equipped\nwith a nonnegative-density reconstruction which allows for vacuum regions\nduring the simulation. We provide several prototypical examples from relevant\napplications highlighting the benefit of our algorithms elucidate also some of\nour analytical results.\n