  Evolution of quark-gluon plasma (QGP) near equilibrium can be described by
the second-order relativistic viscous hydrodynamic equations. Consistent and
analytically verifiable numerical solutions are critical for phenomenological
studies of the collective behavior of QGP in high-energy heavy-ion collisions.
A novel analytical solution based on the conformal Gubser flow which is a
boost-invariant solution with transverse fluid velocity is presented. Due to
the non-linear nature of the equation, the analytical solution is
non-perturbative and exhibits features that are rather distinct from solutions
to usual linear hydrodynamic equations. It is used to verify with high
precision the numerical solution with a newly developed state-of-the-art
$(3+1)$-dimensional second-order viscous hydro code (CLVisc). The perfect
agreement between the analytical and numerical solutions demonstrates the
reliability of the numerical simulations with the second-order viscous
corrections. This lays the foundation for future phenomenological studies that
allow one to gain access to the second-order transport coefficients.
