Localization and momentum dissipation of the momentum artificial viscosity

Determine whether the nonzero momentum artificial viscosity \(\mu_S\) extending into the higher-density regions of an evolved neutron star excessively dissipates momentum when the star is moving, and whether adjusting the parameters \(c_{\mathrm{max}}\), \(n_L\), and \(n_H\) produces a more localized \(\mu_S\).

Background

The paper introduces an artificial-viscosity discontinuous Galerkin method for relativistic hydrodynamics, using separate viscosities $\mu$ and $\mu_S$ for the matter variables and momentum density, respectively. In stable neutron-star evolutions, $\mu_S$ is computed from the smoothness of the conserved momentum variables and is observed to remain nonzero over a region extending into the star's higher-density interior, rather than being confined primarily to the stellar surface where sharp matter gradients occur.

The authors identify this extended support of $\mu_S$ as potentially problematic because it could introduce excessive momentum dissipation if the neutron star is moving. They leave unresolved both whether the observed behavior materially affects moving-star simulations and whether modifying the viscosity parameters $c_{\mathrm{max}}$, $n_L$, and $n_H$ can restrict $\mu_S$ to a more localized region.