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

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• 作者：Christian Obrecht^a ; ^{christian.obrecht@insa-lyon.fr" class="auth_mail" title="E-mail the corresponding author} ; Pietro Asinari^b ; Fré ; dé ; ric Kuznik^a ; Jean-Jacques Roux^a
• 关键词：Computational fluid dynamics ; Link-wise artificial compressibility method ; High-performance computing ; Differentially heated cubic cavity ; CUDA
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：72
• 期：2
• 页码：375-385
• 全文大小：524 K

文摘

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 536³${536}^3$ 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${10}^4$ to 10⁶${10}^6$, the thermal fluxes as well as the flow features are in similar good agreement with reference values from the literature.