Flux conservative simulations of BDNK hydrodynamics

For the first time, we develop a fully flux conservative formulation of Bemfica-Disconzi-Noronha-Kovtun (BDNK) first-order causal and stable relativistic hydrodynamics. This formulation allows for a conservation law equation with no derivatives in the source term that can be solved numerically using the Kurganov-Tadmor algorithm for spatial evolution and a Total Variation Diminishing Runge-Kutta for temporal evolution. Numerical solutions are found for the case of conformal fluids in 1+1 dynamics in Milne coordinates. The dependence of the solutions on the choice of hydrodynamic frame is investigated. Quasi-analytical solutions are used to assess the accuracy of our numerical calculations.