A finite volume method has been developed in this work for solving the conservation equations of argon plasma flows in magnetoplasmadynamic self-field accelerators. These accelerators can be used for interplanetary spaceflight missions because of their high specific impulse and high thrust density, .Calculations for different nozzle geometries show that the diffusion caused by the electron pressure drives the arc out of nozzle-type self-field accelerators and influences the arc attachment on the anode significantly. In agreement with the experiment it has been found that a primary reason for plasma instabilities at high current settings is the depletion of density and charge carriers in front of the anode because of the pinch effect.The calculated thrust data agree well with experimental values, so that the newly developed method can be used for the design and optimization of new thrusters.