流处理机上多种群全Boltzmann问题的间断Galerkin快速谱方法
A discontinuous Galerkin fast spectral method for multi-species full Boltzmann on streaming multi-processors
摘要：
当气体系统的分子相距很远时，例如在微尺度气体流动中，其中表面与体积的比率很高，因此表面力占主导地位，分子-表面相互作用导致形成从表面延伸几个平均自由程的局部摩擦非平衡区域。这类系统的动力学行为可用玻尔兹曼方程精确描述。然而，玻尔兹曼方程的多维性质提出了一个巨大的计算挑战。随着近年来数学的发展和千万亿次尺度的出现，全Boltzmann方程的动力学性质已经变得易于处理。我们提出了一个实施方案，最近推出的多物种不连续Galerkin快速谱（DGFS）方法解决流多处理器上的完整玻尔兹曼。本实施方案在几分钟内求解非齐次Boltzmann方程，使其比目前广泛用于求解Boltzmann方程的最先进的随机方法-直接模拟Monte Carlo-快至少两个数量级。已经提出了各种性能度量，例如弱/强缩放。在36个Nvidia Tesla-P100 GPU上的并行效率为0.96- 0.99。
英文摘要：
When the molecules of a gaseous system are far apart, say in microscale gas flows where the surface to volume ratio is high and hence the surface forces dominant, the molecule-surface interactions lead to the formation of a local thermodynamically non-equilibrium region extending few mean free paths from the surface. The dynamics of such systems is accurately described by Boltzmann equation. However, the multi-dimensional nature of Boltzmann equation presents a huge computational challenge. With the recent mathematical developments and the advent of petascale, the dynamics of full Boltzmann equation is now tractable. We present an implementation of the recently introduced multi-species discontinuous Galerkin fast spectral (DGFS) method for solving full Boltzmann on streaming multi-processors. The present implementation solves the inhomogeneous Boltzmann equation in span of few minutes, making it at least two order-of-magnitude faster than the present state-of-art stochastic method---direct simulation Monte Carlo---widely used for solving Boltzmann equation. Various performance metrics, such as weak/strong scaling have been presented. A parallel efficiency of 0.96--0.99 is demonstrated on 36 Nvidia Tesla-P100 GPUs.
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