High-performance Implementations and Large-scale Validation of the Link-wise Artificial Compressibility Method

The link-wise artificial compressibility method (LW-ACM) is a recent formulation of the artificial compressibility method for solving the incompressible Navier-Stokes equations. Two implementations of the LW-ACM in three dimensions on CUDA enabled GPUs are described. The first one is a modified version of a stateof-the-art CUDA implementation of the lattice Boltzmann method (LBM), showing that an existing GPU LBM solver might easily be adapted to LW-ACM. The second one follows a novel approach, which leads to a performance increase of up to 1.8 compared to the LBM implementation considered here, while reducing the memory requirements by a factor of 5.25. Large-scale simulations of the lid-driven cubic cavity at Reynolds number Re = 2000 were performed for both LW-ACM and LBM. Comparison of the simulation results against spectral elements reference data shows that LW-ACM performs almost as well as multiple-relaxation-time LBM in terms of accurac

Lattice Boltzmann model approximated with finite difference expressions

We show that the asymptotic properties of the link-wise artificial compressibility method are not compatible with a correct approximation of fluid properties. We propose to adapt the previous method through a framework suggested by the Taylor expansion method and to replace first order terms in the expansion by appropriate three or five points finite differences and to add non linear terms. The "FD-LBM" scheme obtained by this method is tested in two dimensions for shear wave, Stokes modes and Poiseuille flow. The results are compared with the usual lattice Boltzmann method in the framework of multiple relaxation times