Thermal link-wise artificial compressibility method: GPU implementation and validation of a double-population model

The link-wise artificial compressibility method (LW-ACM) is a novel formulation of the artificial compressibility method for the incompressible Navier–Stokes equations showing strong analogies with the lattice Boltzmann method (LBM). The LW-ACM operates on regular Cartesian meshes and is therefore well-suited for massively parallel processors such as graphics processing units (GPUs). In this work, we describe the GPU implementation of a three-dimensional thermal flow solver based on a double-population LW-ACM model. Focusing on large scale simulations of the differentially heated cubic cavity, we compare the present method to hybrid approaches based on either multiple-relaxation-time LBM (MRT-LBM) or LW-ACM, where the energy equation is solved through finite differences on a compact stencil. Since thermal LW-ACM requires only the storing of fluid density and velocity in addition to temperature, both double-population thermal LW-ACM and hybrid thermal LW-ACM reduce the memory requirements by a factor of 4.4 compared to a D3Q19 hybrid thermal LBM implementation following a two-grid approach. Using a single graphics card featuring 6 GiB of memory, we were able to perform single-precision computations on meshes containing up to 536^3 nodes, i.e. about 154 million nodes. We show that all three methods are comparable both in terms of accuracy and performance on recent GPUs. For Rayleigh numbers ranging from 104 to 106 , the thermal fluxes as well as the flow features are in similar good agreement with reference values from the literature.