Abstract: By coupling Poisson's equation for the electric potentialfield with flow-field N-S equations through Lorentz force and the jouleheat, numerical simulation of magneto-fluid with low magnetic Reynoldsnumber was carried out. The influence of the Hall effect and the externalcircuit was considered. The Poisson's equation ill-conditioned matrix causedby high Hall parameter was overcomed by LUSGS pretreatment BI-CGSTABalgorithm without pseudo time step. Numerical simulations of two kind ofphenomenon, hypersonic magneto-fluid flow around a circular cylinder whenHall parameter reaching about 10^2 and the energy deposition in scramjetisolator, indicate that external circuit, electrode cooling measures andplasma uniformity have great influence on the electro-magnetic force.