Reduced-order aerodynamic model of a starting plate with discrete-vortex merging

This study employs potential flow theory with a discrete-vortex method to model the unsteady aerodynamics of a flat plate, with a particular focus on the coupled dynamics of leading-edge and trailing-edge vortices (LEVs and TEVs). Through the simulation of an impulsively starting plate at 45 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mo>°</mml:mo></mml:mrow></mml:math> angle-of-attack, we demonstrate that the initial strong lift production maintaining for approximately two chord lengths of travel arises from differential vortex advection rates—rapid TEV shedding generates strong positive lift, while slow LEV movement over the plate produces weaker negative contributions. This finding provides new physical insight into the LEV-induced lift enhancement that it is likely a consequence of reduced negative lift rather than enhanced positive lift generation, as the LEV slows down to become more stable. To reduce computational complexity while preserving physical fidelity, we develop a novel vortex merge algorithm based on conservations of circulation and momentum, coupled with a condition enforcing minimal velocity perturbation to the plate surface. Through comparisons with both single-vortex and full discrete-vortex models, we demonstrate the superior performance of our reduced-order approach in capturing wake structure evolution and predicting unsteady lift, while balancing computational efficiency across a tunable range of precision. The developed model proves especially effective for long-time or small-time-step calculations, offering significant computational savings without compromising the fidelity of vortex dynamics or force predictions.