Numerical simulations of divergence-type theories for conformal dissipative fluids

Abstract

We present the first numerical simulations of the symmetric-hyperbolic theory for conformal dissipative relativistic fluids developed in Lehner et al. [Hyperbolic theory of relativistic conformal dissipative fluids, Phys. Rev. D 97, 024013 (2018)]. In this theory, the information of the fluid dynamics is encoded in a scalar generating function which depends on three free parameters. By adapting the WENO-Z high-resolution shock-capturing central scheme, we present numerical solutions restricted to planar symmetry in Minkowski spacetime, from two qualitatively different initial data: a smooth bump and a discontinuous step. We perform a detailed exploration of the effect of the different parameters of the theory, and numerically assess the constitutive relations associated with the shear viscosity by analyzing the entropy production rate when shocks are produced.