基于高维数值积分和GPU并行的水滴随机喷溅模型

Random splashing model of water droplets based on high-dimensional numerical integration and GPU parallel computing

摘要

【目的】泄洪雾化成为高坝泄洪安全防护需要重点关注的问题。针对传统的水滴随机喷溅模型计算精度低、计算量大的问题，以及水滴分档随机喷溅模型与数论水滴分档随机喷溅模型在工程实践中的局限性【方法】基于佳点集求解高维数值积分的理论，结合GPU并行计算技术，构建了一种新型水滴随机喷溅模型。通过数值试验，对该模型进行了验证。【结果】结果显示：在工况相同且水滴数量保持一致时，该模型的数值解相较于传统模型展现出更小的绝对误差之和，随着水滴数量的增加，绝对误差之和的减少效果大体上愈发显著。当水滴数量超过200万，减幅则稳定在约50%;借助GPU并行计算技术，该模型的计算效率得到了显著增强，达到了约100倍的加速比，特别是在处理更大规模的数据时，该模型的计算时间显著缩短，进一步凸显了其在计算性能上的优势。【结论】结果表明：该模型能够有效处理以四维随机变量为初始条件的计算实例，相较于传统水滴随机喷溅模型，显著提高了计算精度和计算效率，适用于大规模水滴随机喷溅模拟的实际应用。

Abstract

[Objective] Flood discharge atomization has become a critical issue in the safety protection of high dam flood discharge. The aims are to address the issues of low computational accuracy and high computational load in traditional random splashing models of water droplets, as well as the limitations of the graded random splashing model of water droplets and the number theory graded random splashing model of water droplets in engineering practices. [Methods] A novel random splashing model of water droplets was established based on the theory of high-dimensional numerical integration using good point sets, combined with GPU parallel computing technology. The model was verified through numerical experiments. [Results] The result showed that under the same conditions and with the same number of water droplets, the numerical solution of the proposed model exhibited smaller total absolute errors than those of traditional models. As the number of water droplets increased, the reduction in total absolute errors became generally more pronounced. When the number of water droplets exceeded 2 million, the reduction stabilized at approximately 50%. With the aid of GPU parallel computing technology, the computational efficiency of the model was significantly enhanced, achieving an acceleration ratio of about 100 times. Especially when processing larger-scale data, the computational time of the model was significantly reduced, further highlighting its advantage in computational performance. [Conclusion] The findings indicate that the proposed model can effectively handle computational cases with four-dimensional random variables as initial conditions. It significantly improves computational accuracy and efficiency compared to traditional random splashing models of water droplets, making it suitable for practical applications in large-scale simulations of random splashing of water droplets.

关键词

泄洪雾化 / 水滴随机喷溅模型 / 高维数值积分 / 拟蒙特卡洛 / 佳点集 / GPU并行计算 / 计算性能

Key words

flood discharge atomization / random splashing model of water droplets / high-dimensional numerical integration / quasi-Monte Carlo / good point set / GPU parallel computing / computational performance

基金资助

华能集团科技项目TB水电站施工图阶段第一批重大科研项目(HNKJ22-H87)

国家自然科学基金项目(52379077)

中国博士后科学基金项目(2023M732603)

浙江省自然科学基金联合基金项目(LZJWY22E090003)

中国华能集团有限公司科技项目(HNKJ22-H108)