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Smooth profile method (SPM) is well known method for the study of colloids, dispersed in a continuous fluid, using direct numerical simulations (DNS). In this method, Navier-Stokes equation is solved for the fluid in Eulerian frame, whereas particles are traced in lagrangian frame, using Newton’s equation of motion. The rigidity of the particles in maintained, using a body function along with the smooth density function.  The original sharp boundary of particle is replaced with a smooth interface, represented by a density function, having value 0 and 1 in the fluid and particle domains, respectively. In between these limits, this function varies smoothly. This method has been used to study the sedimentation of spherical particles, electrophoresis, shear flows, and recently, it has also been extended to the non-spherical particles (rigid body) and to the non-Newtonian fluid.  We have extensively used this method to study the sedimentation for both spherical and non-spherical particles, at finite Reynolds number.