  Anomalous hydrodynamics is a low-energy effective theory that captures
effects of quantum anomalies. We develop a numerical code of anomalous
hydrodynamics and apply it to dynamics of heavy-ion collisions, where anomalous
transports are expected to occur. This is the first attempt to perform fully
non-linear numerical simulations of anomalous hydrodynamics. We discuss
implications of the simulations for possible experimental observations of
anomalous transport effects. From analyses of the charge-dependent elliptic
flow parameters ($v_2^\pm$) as a function of the net charge asymmetry $A_\pm$,
we find that the linear dependence of $\Delta v_2^\pm \equiv v_2^- - v_2^+$ on
the net charge asymmetry $A_\pm$ cannot be regarded as a robust signal of
anomalous transports, contrary to previous studies. We, however, find that the
intercept $\Delta v_2^\pm(A_\pm=0)$ is sensitive to anomalous transport
effects.
