基于OpenMP的明渠圣维南系统的大规模模拟

Large-Scale Simulation of the Open Channel Saint-Venant System Based on OpenMP

摘要: 了解流道中水流的行为对于早期洪水灾难管理和挽救生命起到了至关重要的作用。本文就是以地表水流作为研究对象，了解洪水的行为。为了预测和模拟洪水的演进过程，利用二维圣维南偏微分方程建立了具有初始条件和边界条件的数学模型。使用显示的有限差分法对模型进行离散化，在时间和空间上均使用中心差分格式，时间上的中心差分也被称作蛙跳格式。之后使用OpenMP对其并行化实现。为了测试和实验的目的，我们使用了一个简单的长方体流道来模拟。通过数值模拟得到不同时间步长下的输出参数，比如水流的高度、速度，之后对这些参数进行处理，实现可视化。最后，将并行程序与串行程序进行对比，进行规模扩展测试。

Abstract: Understanding the flow behavior in the channel plays an important role in early flood disaster management and lifesaving. This paper is aimed at the surface flows to study the behavior of flood waves. In order to predict and simulate the flood process, a mathematical model with initial and boundary conditions is established by using two-dimensional Saint Venant partial differential equations. The explicit finite difference method is used to discretize the model. Here, the central difference scheme is used in both time and space. The central difference scheme in time is also called leapfrog scheme. Then it is implemented and parallelized by MPI and OpenMP. For testing and experimental purposes, we used a simple cuboid tank to simulate an open channel. Through numerical simulation, the output parameters under different time steps, such as the height and speed of the water flow, are obtained, and then these parameters are processed to realize visualization. Finally, the parallel program is compared with the serial program, and the scale expansion test is carried out.