Computation of Unsteady Incompressible Viscous Flows Using Kinetically Reduced Local Navier-Stokes Equations on a GPU

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. The numerical results obtained by the KRLNS equations are compared with those obtained by the pseudo-spectral method (PSM), which is a standard approach to incompressible viscous flows for low Mach number, as well as Lattice Boltzmann Method (LBM). 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 smaller level by giving an appropriately low Mach number. Parallel computation is carried out on a GPU based on NVIDIA Tesla C1060 system and the provided CUDA library.