Higher order numerical simulation of unsteady viscous incompressible flows using kinetically reduced local Navier–Stokes equations on a GPU

• Higher order approach to KRLNS equations are applied for flow simulations.
• The solutions are in excellent agreement with those of the standard approach.
• KRLNS approach can capture the correct transient behavior without sub-iterations.
• KRLNS approach can keep the divergence fluctuation at small level.
• Speedup of parallel computation on a GPU is at least 5.

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.