A computational method for electron fluids in Hall thrusters in two dimensions using a hyperbolic system of conservation laws is proposed. A hyperbolic system is constructed by introducing pseudo-time advancement terms and it is solved by an upwind method and computational techniques to accelerate the convergence. The method is applied to a calculation condition of concave magnetic lines of force like ones in Hall thruster channels. The calculation results reflect the magnetic field geometry and the calculated distributions are proved to be reasonable by the theoretical expectation of thermalized potential. The analysis on pseudo-time advancement terms proves that the method enables robust and fast calculation with preserving the conservation laws in two dimensions.