Multi-GPU parallel computation of unsteady incompressible flows using kinetically reduced local Navier-Stokes equations

Numerical simulations of 2D doubly periodic shear layers and 3D decaying homogeneous isotropic turbulence are presented using Kinetically Reduced Local Navier-Stokes (KRLNS) equations that is applicable to the unsteady incompressible flows without the need for sub-iterations and is capable of capturing the correct transient behavior. To achieve high accuracy, the KRLNS equations is discretized with higher order central difference approximations and 4-stage Runge-Kutta method. The results are compared with the solutions obtained by Lattice Boltzmann method (LBM) and pseudo-spectral method (PSM), which is the standard approach for this problem. Parallel computations are carried out on multiple GPUs (Tesla K40), maximum 4 GPUs available, based on the domain decomposition method and the speedup of the KRLNS equations is investigated. It is found that all three methods can capture the transient flow fields of unsteady incompressible flow and a large speedup for the KRLNS equations is obtained.