The Development and Application of Courant Number on the Two-Dimensional MacCormack Bed Evolution Model

• Main Authors: Yu-Tun Lin, 林鈺敦
• Other Authors: Chang-Tai Tsai
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/06189837997686960101

碩士 === 國立成功大學 === 水利及海洋工程學系 === 87 === Courant Number decides the stability of Explicit Scheme. However, the effect of simulation on the two-dimensional model is rarely calculated. The research mainly discusses the effect of Courant Number on the two-dimensional depth-averaged bed evolution model with MacCormack explicit finite-difference scheme. This model is applied to simulate the flows in two hypothetical channel, laboratory flume, and Pai-chang River . Through the simulation in the laboratory flume, the measured data and the numerical values are quite similar, which indicates this model makes a good simulation. The better numerical values can be got when using The Method of Characteristics on the bound. And this model also has a reasonable simulation in Pai-chang River. From the simulation, it is found that when Courant Number gets increasingly closer to 1, the two-dimensional MacCormack bed evolution model will get a more accuracy conclusion. In the model, Courant Number can be took really close to 1 to save some calculating time. The artificial viscosity can diminish numerical damping results. The affect of artificial viscosity on simulation for velocity and depth is not apparent, However, the conservation of flow discharge will be affected.