摘要
本文将Harten的总变差缩减有限差分格式(TVD),应用于非线性的不可压缩的浅水波方程数值求解。通过对一锥、二维溃坝洪水波的数值模拟,成功地模拟了溃坝问题中的激波和膨胀波现象,保持了解在间断处陡峭,而在其两侧无振动。
The. TVD (Total Variation Diminishing) finite difference method for the shallow water wave equations in one dimension and two dimensions is based on Harten's conservation form equations' TVD idea to simulate gas dynamic shock wave equations extensively and successfully.In this paper, one and two-dimensional shallow water wave conservation form equations are given, TVD idea is applied to these conservation form equations to get the shallow water wave equations' TVD scheme.Successful simulation was made of the shock wave and the rarefraction wave phenom-enona about an one-dimensional dambreaking compulational model and a bugle shaped two-dimensional dam-breaking computational model by using TVD scheme. The numerical solutions of this paper have always preserved sharpness and nonoscillation near the place where the solution is discontinuous.Different results between the two-dimensional model and the one-dimensional model are found, for example, the two-dimensional model's results show a faster descent behind the shock wave and a greater depth near the shore than that in the centre of the river.
出处
《海洋与湖沼》
CAS
CSCD
北大核心
1991年第2期115-123,共9页
Oceanologia Et Limnologia Sinica
