Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios
Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios
复制标题
DOI：
10.1016/j.compfluid.2014.01.004
复制
发表时间：
2014-04
影响因子：
2.8
通讯作者：
Amir Banari;C. Janßen;S. Grilli;M. Krafczyk
中科院分区：
文献类型：
--
作者：
Amir Banari;C. Janßen;S. Grilli;M. Krafczyk
我们提出了一个格子玻尔兹曼方法（LBM）的发展与高密度比的多相流的数值模拟，如海洋表面波和海气相互作用的问题，其高效的实现上的大规模并行通用图形处理单元（GPGPU）。LBM扩展了Inamuro等人的“s（2004）的多相方法，在严格推导的扩散界面模型的基础上求解Cahn-Hilliard方程。与Inamuro等人类似，由高密度比引起的不稳定性通过求解用于流体压力的附加泊松方程来消除。我们首先表明，在GPGPU上获得的LBM结果与标准的分析基准问题吻合良好：（i）无限板之间的两流体层流Poilluille流，其中数值误差表现出预期的收敛性作为空间离散化的函数;和（ii）静止液滴的情况下，这验证了表面张力处理的准确性以及随着网格分辨率的增加其收敛性。然后，一个上升的气泡的模拟同时验证建模的粘性（包括阻力）和表面张力的影响，在流体界面，为非定常流的情况下。最后，数值验证更复杂的流动，如瑞利-泰勒不稳定性和波破碎，进行了研究。在所有情况下，数值结果与参考数据吻合良好，表明新开发的模型可以作为一个精确的工具，用于调查具有高密度比的多相流的复杂物理。重要的是，GPGPU的实现证明了这种类型的模型是非常高效的，从而大大加快了计算时间。虽然只有二维的情况下，计算工作量低，LBM模型可以（并将）在未来的工作中，这使得它非常重要的三维使用一个有效的解决方案。
We present the development of a Lattice Boltzmann Method (LBM) for the numerical simulation of multiphase flows with high density ratios, such as found in ocean surface wave and air–sea interaction problems, and its efficient implementation on a massively parallel General Purpose Graphical Processing Unit (GPGPU). The LBM extends Inamuro’s et al.’s (2004) multiphase method by solving the Cahn–Hilliard equation on the basis of a rigorously derived diffusive interface model. Similar to Inamuro et al., instabilities resulting from high density ratios are eliminated by solving an additional Poisson equation for the fluid pressure. We first show that LBM results obtained on a GPGPU agree well with standard analytic benchmark problems for: (i) a two-fluid laminar Poiseuille flow between infinite plates, where numerical errors exhibit the expected convergence as a function of the spatial discretization; and (ii) a stationary droplet case, which validates the accuracy of the surface tension force treatment as well as its convergence with increasing grid resolution. Then, simulations of a rising bubble simultaneously validate the modeling of viscosity (including drag forces) and surface tension effects at the fluid interface, for an unsteady flow case. Finally, the numerical validation of more complex flows, such as Rayleigh–Taylor instability and wave breaking, is investigated. In all cases, numerical results agree well with reference data, indicating that the newly developed model can be used as an accurate tool for investigating the complex physics of multiphase flows with high density ratios. Importantly, the GPGPU implementation proves highly efficient for this type of models, yielding large speed-ups of computational time. Although only two-dimensional cases are presented here, for which computational effort is low, the LBM model can (and will) be implemented in three-dimensions in future work, which makes it very important using an efficient solution.