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 GiB1  of memory, we were able to perform single-precision computations on meshes containing up to 53635363 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 104104 to 106106, the thermal fluxes as well as the flow features are in similar good agreement with reference values from the literature.