非线性色散方程的局部间断Petrov-Galerkin 方法  

A Local Discontinuous Petrov-Galerkin Method for Nonlinear Dispersive Equations

作　　者：苏晟洁 高巍[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古 呼和浩特

出　　处：《流体动力学》2020年第4期53-61,共9页International Journal of Fluid Dynamics

摘　　要：本文给出数值求解非线性色散偏微分方程K(n, n)的一种方法。空间离散基于局部间断Petrov-Galerkin方法,时间离散基于三阶TVD Runge-Kutta方法。通过数值模拟试验证明该方法达到了最优收敛阶,能够较好地模拟紧孤子传播和碰撞等复杂波的相互作用。In this paper, a numerical scheme is presented to solve the nonlinear dispersive K(n, n) equations. Spatial discretization is based on the local discontinuous Petrov-Galerkin method and temporal discretization is based on the third order accurate TVD Runge-Kutta scheme. Testing cases show that the present scheme achieves the optimal convergence order and complex wave interaction can be simulated well.

关 键 词：非线性色散偏微分方程 局部间断Petrov-Galerkin方法 紧孤子 

分 类 号：TN9[电子电信—信息与通信工程]