基于格子Boltzmann方程的多尺度模型与并行算法

In recent years, some fluid problems and phenomena including multiscale information has emerged along with the rapid development of technology and the wide application of nanotechnology. Due to the multiscale information, the method which based only on a single physical scale gradually becomes difficult to fully and accurately describe the nature of such problems. Therefore, it is important and imperative to develop suitable multiscale models and algorithms for those problems. In this proposal, we construct our multiscale model and discretized method based on a mesoscopic model named the lattice Boltzmann equations. The macroscopic and microscopic information is added by combining the Navier-Stokes equation and the MD method, respectively. A Newton-Krylov type algorithm is considered to solved the discretized nonlinear system. To improve the convergent rate of the Newton algorithm, some nonlinear preconditioner such as the nonlinear elimination are carefully studied. The linear preconditioner based on domain decomposition method is taken to make the Newton-Krylov type algorithm more efficiently and to improve the scalability. Finally, some benchmark problems are simulated on a domestic supercomputer by using tens of thousands of CPU cores.

近年来, 随着科技的飞速发展以及纳米技术的广泛应用, 跨越多种尺度的流体问题和现象先后涌现. 由于这类问题本身包含着多种尺度的物理内涵，仅基于单一物理尺度来研究这类问题, 逐渐变得难以全面并准确刻画这类问题的本质. 研究与之相适应的跨尺度模型和算法的重要性开始彰显. 本项目将基于格子Boltzmann方程这一介观模型, 并综合宏观的Navier-Stokes方程和微观的分子动力学方法, 构建跨尺度的模型, 并设计相应的离散方法. 采用Newton-Krylov类方法求解离散后的非线性代数系统. 为提高Newton算法的收敛速度, 研究非线性消去等非线性预条件子技术; 为提高线性迭代方法的效率和算法的可扩展性, 研究基于区域分解技术的预条件子技术. 针对计算流体力学中的若干经典问题, 在国产并行机上做数万CPU核的并行数值模拟, 预期发表学术论文5篇, 其中国际高水平期刊文章3篇.

近年来, 随着科技的飞速发展以及纳米技术的广泛应用, 跨越多种尺度的流体问题和现象先后涌现. 由于这类问题本身包含着多种尺度的物理内涵，仅基于单一物理尺度来研究这类问题, 逐渐变得难以全面并准确刻画这类问题的本质. 研究与之相适应的跨尺度模型和算法的重要性开始彰显. 本项目将基于格子Boltzmann方程这一介观模型, 并综合宏观的Navier-Stokes方程和微观的分子动力学方法, 构建跨尺度的模型, 并设计相应的离散方法. 采用Newton-Krylov类方法求解离散后的非线性代数系统. 为提高Newton算法的收敛速度, 研究非线性消去等非线性预条件子技术; 为提高线性迭代方法的效率和算法的可扩展性, 研究基于区域分解技术的预条件子技术.