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| 基于GPU加速的三阶有限体积格式管道瞬变流求解模型 |
| GPU-accelerated third-order finite-volume scheme pipe transient flow solver model |
| 投稿时间：2021-11-19 修订日期：2021-12-28 |
| DOI： |
| 中文关键词: GPU加速 有限体积法 瞬变流 ENO格式 长距离输水 |
| 英文关键词:GPU acceleration Finite volume method the transient flow ENO scheme long-distance water delivery |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 为高效、高精度求解长距离输水系统瞬变流变化过程，应用三阶ENO有限体积格式求解一维管道非恒定流方程组，基于Lax-Friedrichs通量裂分法重构界面通量，上下游界面采用虚拟网格技术、结合交叉管网边界条件建立了一套高效、高精度求解管道瞬变流水锤波的数值模型。引入GPU加速技术，实现对大型输水系统的高效计算。通过特征线法、一阶及二阶Godunov有限体积格式对模型进行验证，结果表明三阶ENO格式在极低的Courant 时也能保持较好的间断捕捉性能且无非物理振荡等优点。同时，对Courant 的高度不敏感性，使得模型划分网格时具有高度的灵活性并能显著的提高计算速度。应用GPU加速技术，表明模型在较多网格数时有明显的加速效果，且加速效果随网格数增多而显著。本模型可为长距离输水系统非恒定瞬变过程的高效精准快速模拟预测提供理论支撑。 |
| 英文摘要: |
| In order to efficiently and accurately solve the transient flow change process of long-distance water conveyance system, the third-order ENO finite volume scheme is used to solve the one-dimensional pipeline unsteady flow equations. The interface flux is reconstructed based on the lax-Friedrichs flux splitting method. A set of efficient and numerical models for solving transient water hammer wave in the pipeline with high accuracy. GPU acceleration technology is introduced to realize the efficient calculation of large-scale water conveyance systems. The model is verified by the Method of Characteristics and the first-order and second-order Godunov finite volume schemes. The results show that the third-order ENO scheme can also maintain good discontinuous capture performance at very low Courant without non-physical oscillation. At the same time, it is highly insensitive to Courant, which makes the model highly flexible in meshing and can significantly improve the computing speed. The application of GPU acceleration technology shows that the model has an obvious acceleration effect when the number of grids is large, and the acceleration effect is significant with the increase of the number of grids. The model can provide theoretical support for efficient, accurate and rapid simulation and prediction of the unsteady transient process of the long-distance water conveyance system. |
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