Comparing the first- and second-order theories of relativistic dissipative fluid dynamics using the 1+1 dimensional relativistic flux corrected transport algorithm

Focusing on the numerical aspects and accuracy we study a class of bulk viscosity driven expansion scenarios using the relativistic Navier-Stokes and truncated Israel-Stewart form of the equations of relativistic dissipative fluids in 1+1 dimensions. The numerical calculations of conservation and transport equations are performed using the numerical framework of flux corrected transport. We show that the results of the Israel-Stewart causal fluid dynamics are numerically much more stable and smoother than the results of the standard relativistic Navier-Stokes equations.