浅水波传播问题的动力学分析与数值计算
发布时间：2018-11-28 20:44
【摘要】：b族方程概括了一大类浅水波动力学问题,研究发现其中的Camassa-Holm方程(b=2)和Degasperis-Procesi方程(b=3)均存在稳定传播的尖波解。在已有b族方程统一对称形式的基础上,针对b=0这一特殊情形,构造了一种等价于多辛Box格式的新隐式多辛格式,用于探索这一特殊情形下b族方程是否存在稳定传播的尖波解。通过数值模拟,一方面,验证了构造的隐式多辛格式具有很好的保结构性能和良好的长时间数值稳定性;另一方面,从数值模拟结果中发现在b=0这一特殊情形下,b族方程不存在稳定传播的尖波解。
[Abstract]:A large class of wave mechanics problems in shallow water are generalized by B-family equations. It is found that both the Camassa-Holm equation (bn _ 2) and the Degasperis-Procesi equation (n _ 3) have sharp wave solutions for stable propagation. On the basis of the unified symmetric form of the B-family equation, a new implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed for the special case of BX _ 0. It is used to explore whether there is a sharp wave solution for the stable propagation of the b family equation in this special case. Through numerical simulation, on the one hand, it is verified that the implicit multi-symplectic scheme has good guaranteed structure performance and good numerical stability for a long time. On the other hand, from the numerical simulation results, it is found that there is no sharp wave solution for the stable propagation of the b family equation under the special case of BX 0.
【作者单位】： 西北工业大学理学院;西北工业大学力学与土木建筑学院;
【基金】：国家自然科学基金(11672233、11302169、11372253) 陕西省自然科学基金(2015JM1026) 航天支撑技术基金(2015-HT-XGD)资助
【分类号】：O175
，
本文编号：2364212
[Abstract]:A large class of wave mechanics problems in shallow water are generalized by B-family equations. It is found that both the Camassa-Holm equation (bn _ 2) and the Degasperis-Procesi equation (n _ 3) have sharp wave solutions for stable propagation. On the basis of the unified symmetric form of the B-family equation, a new implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed for the special case of BX _ 0. It is used to explore whether there is a sharp wave solution for the stable propagation of the b family equation in this special case. Through numerical simulation, on the one hand, it is verified that the implicit multi-symplectic scheme has good guaranteed structure performance and good numerical stability for a long time. On the other hand, from the numerical simulation results, it is found that there is no sharp wave solution for the stable propagation of the b family equation under the special case of BX 0.
【作者单位】： 西北工业大学理学院;西北工业大学力学与土木建筑学院;
【基金】：国家自然科学基金(11672233、11302169、11372253) 陕西省自然科学基金(2015JM1026) 航天支撑技术基金(2015-HT-XGD)资助
【分类号】：O175
，
本文编号：2364212
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