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The behavior of the moving electric arc in low-voltage switching devices is determined by the complex interactions of magnetic forces, current flow, gas flow, heat conduction, and radiation. In this paper three-dimensional simulations of arc motion between parallel arc runners are presented, which consider all these interactions. These simulations are carried out with a computational fluid dynamics (CFD) finite volume code. Based on earlier simulations by Frank Karetta the magnetic field, expressed as vector potential formulation, is now treated by the same type of general transport equations as the other processes, which allows the direct implementation into the CFD package used. This enables one to include the effect of ferromagnetic material in the arc chamber, such as ferromagnetic flux concentrators or steel splitter plates. Typical simulation examples are presented for different design details.