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• A novel model of using nSFEM and DPM to solve particle-laden flows. • The super robustness in handling extremely distorted polygonal meshes of the present method. • The unified implementation of mean value coordinates interpolation as shape function and fluid drag interpolation with high-fidelity. • The polygon mesh in this paper shows a great adaptation to complex geometry. In this work, an n-sided polygonal smoothed finite element method (nSFEM) using mean value shape function for concave polygonal element coupled with the discrete phase model (DPM) is developed to solve particle-laden flows. The fluid phase is solved using nSFEM stabilized by the well-developed characteristic-based split (CBS) algorithm. The concave polygonal element is successfully constructed via the intrinsic characteristic of mean value shape function and a new smoothing domain (SD) construction with more physical meaning; thus, addressing the severely distorted local mesh, as well as retaining good geometric adaptability. In the meantime, the modeling of the coupling between the fluid and the particle is achieved by reusing the mean value interpolation to obtain the fluid drag force acting on the particle. The accurate capture of fluid velocities at particle positions within arbitrary polygonal elements via mean value interpolation ensures fluid drag with high-fidelity. Several classical numerical examples, including particle-laden flow around a circular cylinder, are presented to demonstrate the high accuracy and good robustness, and the capability of the proposed method for predicting particle motion in the analysis of complex particle-laden flows. [ABSTRACT FROM AUTHOR]