二维溃坝绕流的WENO格式数值模拟

WENO(Weighted essentially non-oscillatory scheme)格式是一类新的高精度无振荡差分格式.本文将WENO格式和Runge-Kutta时间离散的思想应用于二维浅水方程组的求解,数值模拟矩形河道中大坝瞬间局部溃倒,下游有障碍物的洪水演进过程,并对模拟结果进行了分析,表明采用WENO格式所建立的高分辨率模型能够有效地模拟溃坝波的演进过程.     

混凝土面板砂砾石坝漫顶溃坝数值模拟

通过溃坝案例的现场调查和水槽模型试验，建立了面板砂砾石坝漫顶溃坝数学模型，以模拟水流特性、砂砾石料以及混凝土面板三者之间的相互作用。该模型主要由3部分组成：(1)考虑漩涡水流和砂砾石料之间的冲蚀特性，引入RNG k-ε湍流模型模拟漩涡水流的反向侵蚀；(2)通过泥沙输移公式和流体体积法(VOF法)追踪砂粒与水流侵蚀交界面，并考虑了砂砾石料的孔隙特性；(3)基于弯矩平衡法判定混凝土面板在自重和水荷载作用下的破坏过程。通过水槽模型试验对数学模型进行验证，结果表明，建立的数学模型能够准确地模拟溃决过程中漩涡水流对大坝的反向侵蚀和面板溃口的详细演化过程；该模型计算的溃口流量、堆石体溃口的发展、溃坝历时以及面板的折断长度，与实测数据的相对误差均小于15%,验证了模型的合理性。与参数化模型相比，本研究提出的溃坝模拟数学模型具有更详细的结果。     

Simulation Study on Dam Break Flow Based on the B-Spline Material Point Method北大核心CSCD

The dam break flow poses a common free surface flow problem in hydraulic engineering, and its ac⁃ curate simulation is of great engineering significance. The B⁃spline material point method (BSMPM), as an im⁃ proved algorithm of the material point method (MPM), has optimized accuracy and convergence in material point calculations and unique algorithmic advantages in free surface flow problems. Based on the BSMPM, a weakly compressible BSMPM (WC⁃BSMPM) was developed through introduction of an artificial equation of state. The simulation of the dam break flow problem was carried out, with the effects of the order of the B⁃ spline interpolation basis function on the simulation results analyzed. The results show that, the simulated fluid wavefront position, the wavefront velocity and the elevation variation at a given position are basically consistent with the existing experimental results. As the order of the basis function increases, the computation time will lengthen for about 1.5 times. However, the computation times of the BSMPM of different orders will uniformly increase approximately linearly with the background grid size. The validity of the WC⁃BSMPM simulation of the dam break flow problem was verified. The research provides a new idea and method for the simulation of dam break flow problems. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.