Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria
Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria
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DOI：
10.1098/rsta.2019.0559
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发表时间：
2020-07-10
期刊：
影响因子：
5
通讯作者：
Parmigiani, Andrea
中科院分区：
文献类型：
--
作者：
Latt, Jonas;Coreixas, Christophe;Parmigiani, Andrea
提出了一种基于双分布函数的格子Boltzmann方法（DDF-LBM），用于模拟超音速多原子气体。该模型依赖于自20世纪90年代末以来被广泛使用的离散速度方法的数值平衡。在这里，它被扩展到再现任意数量的矩的麦克斯韦-玻尔兹曼分布。这些扩展标准的5约束（质量，动量和能量）的方法导致正确的模拟热，可压缩流只有39个离散的速度在3D中。这个BGK-LBM的稳定性是通过依赖于分析计算的克努森数依赖的弛豫时间来加强的。因此，高雷诺数，超音速流可以模拟在一个有效的和优雅的方式。虽然一维黎曼问题表明所提出的方法能够处理零粘度极限下的不连续性，但NACA 0012翼型的超音速流模拟证实了该模型在低粘度和超音速状态下的优异性能。通过一个球体的流动进一步模拟调查的三维行为，我们的模型在低粘度的超音速制度。所提出的模型被证明是更有效的比以前的5时刻D3 Q343 DDF-LBM的CPU和GPU架构。然后，它开辟了一个全新的世界，可压缩流的应用，可以现实地处理一个纯粹的LB方法。这篇文章是“流体动力学，软物质和复杂系统：最近的结果和新方法”主题的一部分。
A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on a numerical equilibrium that has been extensively used by discrete velocity methods since the late 1990s. Here, it is extended to reproduce an arbitrary number of moments of the Maxwell-Boltzmann distribution. These extensions to the standard 5-constraint (mass, momentum and energy) approach lead to the correct simulation of thermal, compressible flows with only 39 discrete velocities in 3D. The stability of this BGK-LBM is reinforced by relying on Knudsen-number-dependent relaxation times that are computed analytically. Hence, high Reynolds-number, supersonic flows can be simulated in an efficient and elegant manner. While the 1D Riemann problem shows the ability of the proposed approach to handle discontinuities in the zero-viscosity limit, the simulation of the supersonic flow past a NACA0012 aerofoil confirms the excellent behaviour of this model in a low-viscosity and supersonic regime. The flow past a sphere is further simulated to investigate the 3D behaviour of our model in the low-viscosity supersonic regime. The proposed model is shown to be substantially more efficient than the previous 5-moment D3Q343 DDF-LBM for both CPU and GPU architectures. It then opens up a whole new world of compressible flow applications that can be realistically tackled with a purely LB approach. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.