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A major research program underway at Loughborough University involves the generation of ultrahigh magnetic fields up to 300 T (3 MG) by means of magnetic flux-compression. A high pulsed current is discharged into a single-turn driving coil surrounding a liner, with various aspects of the associated practical work being presented in a companion paper. This paper explains the two-dimensional filamentary modeling technique that is used to provide detailed prediction of the liner implosion, driving coil dynamics and magnetic field diffusion through all the metallic elements of the arrangement. The main typical results from numerical experiments are presented and experimental data are compared with theoretical predictions.