We present a highly optimized thread-safe lattice Boltzmann model in which the non-equilibrium part of the distribution function is locally reconstructed via recursivity of Hermite polynomials. Such a procedure allows the explicit incorporation of non-equilibrium moments of the distribution up to the order supported by the lattice. Thus, the proposed approach increases accuracy and stability at low viscosities without compromising performance and amenability to parallelization with respect to standard lattice Boltzmann models. The high-order thread-safe lattice Boltzmann is tested on two types of turbulent flows, namely, the turbulent channel flow at Reτ=180 and the axisymmetric turbulent jet at Re = 7000; it delivers results in excellent agreement with reference data [direct numerical simulations (DNS), theory, and experiments] and (a) achieves peak performance [∼5×1012 floating point operations (FLOP) per second and an arithmetic intensity of ∼7 FLOP/byte on a single graphic processing unit] by significantly reducing the memory footprint, (b) retains the algorithmic simplicity of standard lattice Boltzmann computing, and (c) allows to perform stable simulations at vanishingly low viscosities. Our findings open attractive prospects for high-performance simulations of realistic turbulent flows on GPU-based architectures. Such expectations are confirmed by excellent agreement among lattice Boltzmann, experimental, and DNS reference data.

中文翻译：

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用于高性能计算湍流模拟的高阶线程安全格子玻尔兹曼模型

我们提出了一种高度优化的线程安全格子玻尔兹曼模型，其中分布函数的非平衡部分通过 Hermite 多项式的递归性进行局部重构。这样的过程允许将分布的非平衡矩显式合并到晶格支持的阶数。因此，所提出的方法提高了低粘度下的准确性和稳定性，而不会影响相对于标准格子玻尔兹曼模型的性能和并行化的适应性。高阶线程安全格子玻尔兹曼在两种湍流上进行了测试，即Reτ=180时的湍流通道流和Re=7000时的轴对称湍流射流；它提供的结果与参考数据[直接数值模拟 (DNS)、理论和实验] 非常一致，并且 (a) 实现了峰值性能 [每秒约 5×1012 次浮点运算 (FLOP)，算术强度为约 7 FLOP /单个图形处理单元上的字节]通过显着减少内存占用，（b）保留了标准格子玻尔兹曼计算的算法简单性，并且（c）允许在极低的粘度下执行稳定的模拟。我们的研究结果为基于 GPU 的架构上真实湍流的高性能模拟开辟了诱人的前景。格子玻尔兹曼、实验和 DNS 参考数据之间的良好一致性证实了这种预期。