Particle-laden flows are ubiquitous in natural and industrial processes, such as ice crystal settling and polymer manufacturing[1,2], where particles often feature non-circular cross-sections. Traditional numerical models struggle with the unified description of irregular geometries, grid dependency, and the accurate capture of shape-induced hydrodynamic interactions in multi-particle systems. This study develops an integrated numerical framework combining a Geometric Representation Model (GRM), the immersed boundary method, and a Characteristic-Based Splitting (CBS) scheme[3]. The GRM unifies complex geometry descriptions via straight and curved segments, while the IBM eliminates grid dependency through localized information exchange. The CBS scheme ensures stable solutions for the incompressible Navier-Stokes equations, with the overall framework rigorously validated against benchmark cases. Systematic investigations reveal: (1) For isolated particles, geometry significantly modulates lift/drag coefficients and vortex shedding; these effects are most pronounced for polygons with n < 6 and diminish as side numbers increase. (2) In tandem triangular-circular systems, spacing (1D–3D) and shape factors(Wcur) (0.05–0.60) govern flow regimes, with Wcur = 0.4 serving as a critical threshold for minimum drag and increased spacing triggering a transition from shear-layer reattachment to co-shedding[4]. (3) Particle morphology and orientation dictate sedimentation; curved quadrilaterals exhibit higher settling velocities than rectangles and demonstrate distinct regulatory effects on tumbling and stable descent modes.This work provides a robust tool for simulating generalized particle flows, elucidating shape-driven mechanisms to support the optimization of industrial processes.