  The Chiral Magnetic Effect (CME) is a macroscopic manifestation of
fundamental chiral anomaly in a many-body system of chiral fermions, and
emerges as anomalous transport current in the fluid dynamics framework.
Experimental observation of CME is of great interest and has been reported in
Dirac and Weyl semimetals. Significant efforts have also been made to look for
CME in heavy ion collisions. Critically needed for such search, is the
theoretical prediction for CME signal. In this paper we report a first
quantitative modeling framework, the Anomalous Viscous Fluid Dynamics (AVFD),
which computes the evolution of fermion currents on top of realistic bulk
evolution in heavy ion collisions and simultaneously accounts for both
anomalous and normal viscous transport effects. The AVFD allows a quantitative
understanding of the generation and evolution of CME-induced charge separation
during hydrodynamic stage as well as its dependence on theoretical ingredients.
With reasonable estimates of key parameters, the AVFD simulations provide the
first phenomenologically successful explanation of the measured signal in
200AGeV AuAu collisions.
