Flow control based on time-dependent magnetic fields is used in various industrial processes involving liquid metals, i. e. during the solidification process of silicon to improve the quality and efficiency of wafers. In order to investigate the interactions between spatiotemporal-varying magnetic fields and conductive fluids numerical simulations are performed. The numerical models are verified by model experiments with opaque low-melting alloys. A suitable measurement technique for flow mapping in such model experiments is ultrasound Doppler velocimetry. In contrast to conventional systems employing transducers with fixed sound field our approach is to use a phased array with the ability to focus and steer its acoustic field. We present the Phased Array Ultrasound Doppler Velocimeter (PAUDV) for flow mapping in magnetohydrodynamics. With its custom host software for control and signal processing experiments that are flexible regarding the experimental setup can be defined.