This paper addresses a new suspension balance direct-forcing immersed boundary model (SB-DF-IBM), for wet granular flows over obstacles. We mean by "wet granular" term all non-Newtonian flows that are made of non-Brownian particles (rigid spheres) immersed in a Newtonian fluid. This new SB-DF-IBM couples the Suspension Balance Model (SBM) to a Direct-Forcing Immersed Boundary Method (DF-IBM). The mathematical formulation in this contribution is based on a mixed Eulerian-Lagrangian approach. A novel feature of this new formulation is that many Lagrangian particles of the same size of the suspended particles, can be introduced into the continuum medium. This extrapolates the physics from a macroscopic to a microscopic scale, making the SB-DF-IBM behaves as a Dynamic-Scale Model (DSM). This SB-DF-IBM is implemented, as a new solver, in the OpenFOAW (R) open-source Computational Fluid Dynamics (CFD) software. Then, a numerical study is conducted on isodense mono-dispersed suspension flows over a stationary cylinder, in both wide and micro-channels, to test the functionality and performances of this SB-DF-IBM. The pressure difference, drag and lift forces are addressed for different initial bulk concentrations between 0% and 50%. Moreover, the effect of a cylindrical obstacle on the suspension flow separation in a microchannel is analyzed. The numerical results are presented and compared to recent experimental measurements from the literature addressing the non-Newtonian response of a suspension flow. As a conclusion, this SB-DF-IBM is a promising tool that can be introduced into different CFD packages for simulating wet granular non-Newtonian flows over obstacles. (C) 2016 Elsevier B.V. All rights reserved.