非线性发展方程非守恒格式的计算稳定性

Computational Stability of Non-Conservative Schemes of Nonlinear Evolution Equations

针对非线性发展方程的非守恒格式 ,以二维非线性浅水波方程为例 ,给出了计算稳定的必要性条件 .在数值试验的基础上 ,进一步讨论了非线性发展方程非守恒格式与初值之间的关系 .理论分析和数值试验证明 ,非守恒格式的计算稳定性不仅与格式的结构有关 。

For the non conservative schemes of nonlinear evolution equations, taking two dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given. Based on the numerical tests, the relationship between the nonlinear computational stability, the construction of difference schemes, and the form of initial values is further discussed. It is proved through theoretical analysis and numerical tests that the computational stability of non conservative schemes is not only dependent on the structure of the scheme, but also on the form of initial values and their partial derivatives.