We present a consistent mesh-free numerical scheme for solving the incompressible Navier–Stokes equations. Our method is based on entropically damped artificial compressibility for imposing the incompressibility constraint explicitly, and the Discretization-Corrected Particle Strength Exchange (DC-PSE) method to consistently discretize the differential operators on mesh-free particles. We further couple our scheme with Brinkman penalization to solve the Navier–Stokes equations in complex geometries. The method is validated using the 3D Taylor–Green vortex flow and the lid-driven cavity flow problem in 2D and 3D, where we also compare our method with hr-SPH and report better accuracy for DC-PSE. In order to validate DC-PSE Brinkman penalization, we study flow past obstacles, such as a cylinder, and report excellent agreement with previous studies.