The turbocharged piston-driven engines are widely used in high altitude long endurance unmanned aerial vehicles (HALE UAVs). Repeated actions of engine pistons and valves give rise to engine pulsations resulting in intensive unsteady flows in the turbocharger. One-dimensional (1-D) modeling, which is computationally effective, plays a crucial role in evaluating turbocharger performance and conducting turbocharger-engine matching under pulsating conditions. The present work introduces a newly developed 1-D software (TURBODYNA) for the sake of improving traditional 1-D modeling's accuracy and generality. The advantages and capabilities of TURBODYNA are illustrated by applying it to three different and typical sorts of turbocharger applications: the single-entry turbine, the twin-entry turbine, and the centrifugal compressor. The unsteady testing conditions include high frequent pressure pulses for the single-entry turbine, out-of-phase pressure pulses for the twin-entry turbine, and rotating stall and surge for the centrifugal compressor. Results show that, by contrast to traditional 1-D modelings, the current 1-D modeling has achieved exceptional improvements in both accuracy and applicability. The novel and powerful tool provides a solid framework for assessing turbocharger unsteady performances and addressing turbocharger-engine matching.