基于GPU加速的三阶有限体积格式管道瞬变流求解模型

为高效和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并结合交叉管网边界条件建立了一套高效和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数时也能保持较好的间断捕捉性能且无非物理振荡。同时,对Courant数的高度不敏感性,使得模型划分网格时具有高度的灵活性并能显著提高计算速度。应用GPU加速技术,发现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。本文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。

GPU-accelerated third-order finite-volume scheme pipe transient flow solver model

In order to efficiently and accurately solve the transient flow change process of a 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 are established.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 performance of discontinuous capture at very low Courant without non-physical oscillation.At the same time,it is highly insensitive to Courant,making the model highly flexible in meshing and significantly improving 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 in the number of grids.The model can provide theoretical support for efficient,accurate,and rapid simulation and prediction of the unsteady transient process of a long-distance water conveyance system.