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For the numerical simulation of magnetoplasmadynamic (MPD) self‐field thruster flow, the solution of one of the two dynamical Maxwell equations – Faraday's law – is required. The Maxwell equations and Ohm's law for plasmas can be summarized in one equation for the stream function so that the two‐dimensional, axisymmetric magnetic field can be calculated. The finite volume (FV) discretization of the equation on unstructured, adaptive meshes is presented in detail and solutions for different thruster currents are shown. The calculated thrust is compared with the experimental data.