HIGH-ORDER WELL-BALANCED FINITE-VOLUME SCHEMES FOR HYDRODYNAMIC EQUATIONS WITH NONLOCAL FREE ENERGY

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.