Optimized finite difference method with artificial dissipation for under-resolved unsteady incompressible flow computations using kinetically reduced local Navier-Stokes equations

Abstract

Abstract Under-resolved unsteady incompressible flow computations employed on coarser grids are presented. Kinetically Reduced Local Navier-Stokes (KRLNS) equations is a newly method to deal with unsteady incompressible flows, which is applicable to the unsteady incompressible flows without the need for sub-iterations and is capable of capturing the correct transient behavior. To stabilize the computations and achieve high accuracy, the KRLNS equations is discretized with higher order standard and optimized types of central finite difference method (FDM) together with artificial dissipation or spatial filter and is integrated by using 4-stage Runge-Kutta method. Numerical simulations of 2D doubly periodic shear layers are carried out on coarser regular grids and the computed solutions are compared with those obtained on finer grids. The parallel computations are implemented on multiple GPU (Tesla K40) system with 4 GPUs, based on the domain decomposition method and the acceleration is investigated. It is found that the solution obtained by optimized type of FDM is more accurate than that of standard one especially for much coarser grids, and that the proposed approach is easy to perform the parallel computations and obtain a large acceleration according to the number of GPUs used.