Artificial resistance of Eulerian-Lagrangian method in 3D numerical model
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摘要: 在三维数模的实践中,发现使用欧拉-拉格朗日方法(ELM)离散对流项会引发计算水位随时间步长减小而增大的异常现象,本文结合数值实验和数学分析对其进行了阐明和研究。数学推导分析表明,这些异常是由于ELM中的线性插值与水平流速的非线性垂线分布之间的不适应所致,插值误差随着插值点离单元侧面距离的减小而增大。在此基础上,对异常现象的本质进行了解释。此外,通过使用垂向σ坐标网格上的三维水动力学模型进行计算,得出ELM的时间阻力现象具有普遍性,但对边界适应能力强的网格系统可以减轻其影响。Abstract: The artificial resistance of the Eulerian-Lagrangian Method (ELM) in a 3D hydrodynamic model is observed and characterized by a rising free-surface elevation when the time step decreases. The phenomenon is illustrated and investigated by combining the numerical experiments and the formal analysis. The analysis indicates that the abnormality results from the linear interpolation of the ELM which does not match the nonlinear distribution of the velocity. Based on the analysis, the phenomena are explained. Moreover, the computations by a 3D hydrodynamic model using the sigma-coordinate indicate that the artificial resistance of the ELM is universal, but the grid which follows the topography and free surface better will alleviate its negative influence.
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Key words:
- hydraulics /
- numerical methods /
- three-dimensional /
- Eulerian-Lagrangian method /
- artificial resistance
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