Although friction stir welding (FSW) is widely employed in aerospace and other engineering fields owing to its ability to produce high-quality joints and low residual stresses, the understanding of its physical mechanisms remains limited by the intense material flow during welding, which lags behind engineering practice. This gap motivates researchers to develop thermo-mechanical coupling models to elucidate the underlying physics, aiming to expand its application boundaries. During FSW, the material undergoes a highly rapid flow-deposition process that is completed within a few seconds. In this study, we present a fully coupled thermo-mechanical-fluid model for friction-stir-welded 2219-T87 aluminum alloy to demonstrate the complete material transport path in the vicinity of the tool. A particle-tracking algorithm was employed to quantitatively analyze the flow and subsequent refilling trajectory of the tracer material. The predicted temperature history and flow-zone geometry showed close agreement with experimental data. At the axis Z = 7 mm, the peak downward vertical velocity of the material reached 16.57 mm/s at the advancing side of the pin, whereas the peak upward vertical velocity reached 10.47 mm/s at the retreating side. The analysis revealed that the flow-deposition behavior of the material was highly position dependent. The material adjacent to the shoulder followed a multi-loop spiral trajectory around the tool, during which the loop radius gradually decreased and the material migrated markedly downward in the vicinity of the pin. Ultimately, all deposits accumulated on the advancing side. In contrast, the material far from the shoulder exhibited a through-flow pattern, depositing behind the pin without completing a full revolution. Post-weld deposits originating from the advancing side remained on the advancing side, whereas those from the retreating side settled on the retreating side.