Higher order approach of Kinetically Reduced Local Navier Stokes (KRLNS) equations are applied for two-dimensional (2-D) simulations of Womersley problem and doubly periodic shear layers in order to demonstrate the accuracy, efficiency and the capability to capture the correct transient behavior for unsteady incompressible viscous flows. The numerical results obtained by the KRLNS equations using higher order difference approximations are in excellent agreement with those obtained by the Lattice Boltzmann method (LBM) and the pseudo-spectral method (PSM), which is a standard approach to incompressible viscous flows. It is confirmed that the KRLNS method can capture the correct transient behavior without use of sub-iterations due to a smoothing effect introduced by using the Grand potential in the continuity equation, and keep the fluctuation of velocity divergence at small level by taking sufficiently low Mach number. Parallel computations are carried out on a GPU based on NVIDIA Tesla C1060 system and the provided CUDA library. High values of speedup are obtained for three methods, the KRLNS equations, PSM and LBM. (C) 2014 Elsevier Ltd. All rights reserved.