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
DOI: 10.12677/IJFD.2020.84006, PDF,    科研立项经费支持
作者: 苏晟洁, 高 巍：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: 非线性色散偏微分方程；局部间断Petrov-Galerkin方法；紧孤子；Nonlinear Dispersive Equations； Local Discontinuous Petrov-Galerkin Method； Compacton
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。
Abstract: 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.
文章引用：苏晟洁, 高巍. 非线性色散方程的局部间断Petrov-Galerkin 方法[J]. 流体动力学, 2020, 8(4): 53-61. https://doi.org/10.12677/IJFD.2020.84006

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