  We construct a dynamical model for high-energy heavy-ion collision based on
the relativistic resistive magneto-hydrodynamic framework. Using our newly
developed (3+1)-dimensional relativistic resistive magneto-hydrodynamics code,
we investigate magneto-hydrodynamic expansion in symmetric and asymmetric
collision systems as a first application to high-energy heavy-ion collisions.
As a realistic initial condition for electromagnetic fields, we consider the
solutions of the Maxwell equations with the source term of point charged
particles moving in the direction of the beam axis, including finite constant
electrical conductivity of the medium. We evaluate the directed flow in the
symmetric and asymmetric collisions at RHIC energy. We find a significant
effect of finite electrical conductivity on the directed flow in the asymmetric
collision system. We confirm that a certain amount of energy transfer by
dissipation associated with Ohmic conduction occurs in the asymmetric collision
system because of asymmetry of the electric field produced by two different
colliding nuclei. Because this energy transfer makes the pressure gradient of
the medium flatter, the growth of directed flow decreases.
