Various industrial processes in the field of metallurgy and crystal growth use magnetic fields in order to manipulate liquid flows of electrically conductive melts. Ultrasound is frequently used for flow process monitoring. However the temporal and the spatial resolutions of commercially available ultrasound measurement systems are not sufficient to monitor complex vortex structures or turbulent flows. This article presents a novel modular Ultrasound-Array-Doppler-Velocimeter which allows multi-dimensional multi- component measurements of such flows. Using four ultrasound transducer arrays, each with 25 piezoelements, and a parallelized measurement technique (time division multiplex) it is possible to achieve frame rates of 28 Hz with a spatial resolution of 3 mm. Due to this procedure novel chances arise for a deeper understanding of complex flow processes in magnetohydrodynamics.