  We present the first numerical simulations of the symmetric--hyperbolic
theory for conformal dissipative relativistic fluids developed in [1]. 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 show 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.
