  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.
