Matter with chiral fermions is microscopically described by theory with quantum anomaly and macroscopically described (at low energy) by anomalous hydrodynamics. For such systems in the presence of external magnetic field and chirality imbalance, a charge current is generated along the magnetic field direction --- a phenomenon known as the Chiral Magnetic Effect (CME). The quark-gluon plasma created in relativistic heavy ion collisions provides an (approximate) example, for which the CME

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... s a charge separation perpendicular to the collisional reaction plane. Charge correlation measurements designed for the search of such signal have been done at RHIC and the LHC for which the interpretations, however, remain unclear due to contamination by background effects that are collective flow driven, theoretically poorly constrained, and experimentally hard to separate. Using anomalous (and viscous) hydrodynamic simulations, we make a first attempt at quantifying contributions to observed charge correlations from both CME and background effects in one and same framework. The implications for the search of CME are discussed.