王玉英, 王金环, 杨汉春. 2维非凸标量守恒律分3片黎曼问题的数值解[J]. 云南大学学报(自然科学版), 2010, 32(6): 633-638 .
引用本文: 王玉英, 王金环, 杨汉春. 2维非凸标量守恒律分3片黎曼问题的数值解[J]. 云南大学学报(自然科学版), 2010, 32(6): 633-638 .
WANG Yu-ying, WANG Jin-huan, YANG Han-chun. Numerical solutions of Riemann problems in three pieces for two-dimensional nonconvex scalar conservation laws[J]. Journal of Yunnan University: Natural Sciences Edition, 2010, 32(6): 633-638 .
Citation: WANG Yu-ying, WANG Jin-huan, YANG Han-chun. Numerical solutions of Riemann problems in three pieces for two-dimensional nonconvex scalar conservation laws[J]. Journal of Yunnan University: Natural Sciences Edition, 2010, 32(6): 633-638 .

2维非凸标量守恒律分3片黎曼问题的数值解

Numerical solutions of Riemann problems in three pieces for two-dimensional nonconvex scalar conservation laws

  • 摘要: 考虑2维非凸标量守恒律初值为3片常数的黎曼问题,使用WENO和Runge-Kutta格式,对具有Guckenheimer结构现象的解进行数值分析,所得数值结果清晰地展示了Guckenheimer结构由激波之间的整体相互作用形成的数学机制,从而揭示了Guckenheimer结构这一重要的2维非线性现象.

     

    Abstract: The Riemann problems with three pieces of constants for two-dimensional nonconvex scalar conservation laws are considered.By using WENO and Runge-Kutta schemes,numerical analysis of solutions involving Guckenheimer structure is presented,the numerical results clearly exhibit the mathematical mechanism of Guckenheimer structure made up of global interactions among the shock waves.Thus the important nonlinear phenomenon of Guckenheimer structure of solutions under two dimensions is shown numerically.

     

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