In recent years, ablative plasma generated by capillary discharge attracted considerable attention because of its possible applications in electrothermal launchers, laser-driven particle accelerators, thin-film deposition and soft X-ray lasers, etc. An electrical discharge through a capillary insulator heats the capillary plasma that provides further evaporation of the capillary wall and electrode. The created plasma is confined by the capillary wall, electrode material and flow in a specified chamber through a hollow electrode. The mass flux leaving the capillary in axial motion is replenished by a radial inward flow of matter. Thus the radial component of the mass flux plays a principal role in the mass and energy balance. In this paper, we present a theoretical model for a time-dependent magneto-hydrodynamical simulation to calculate the dynamic evolution of plasma flow and transportation in two-dimensional configurations combined with turbulent effect. The thermodynamic and transport properties are characterized by a model that describes the plasma composition, equation of state, internal energy, viscosity and thermal and electrical conductivity for a partially ionized multi-component plasma in the weakly non-ideal region, similar to that which exists in the ablation-controlled arcs. Our model results show that some of the well-known experimental features of this kind of discharge are confirmed, particularly the radial mass and energy transportation.