Artificial boundary method for the Zakharov-Rubenchik equations
Artificial boundary method for the Zakharov-Rubenchik equations
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DOI：
10.1007/s11075-023-01739-y
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发表时间：
2024-01
影响因子：
2.1
通讯作者：
Hongwei Li;Xiangyu Zhang
中科院分区：
文献类型：
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作者：
Hongwei Li;Xiangyu Zhang
研究了无界区域上Zakharov-Rubenchik方程的数值解，该方程模拟了等离子体物理中两种波的传播.基于双曲型方程组和非线性Schr dinger方程的算子分裂法和人工边界法的思想，在人工边界上设计Zakharov-Rubenchik方程的人工边界条件，将无界区域上的原问题转化为有界计算区域上的初边值问题，并利用有限差分法进行有效求解.引入一系列辅助变量，通过能量估计严格分析了约化初边值问题的稳定性。数值算例验证了人工边界条件的有效性，验证了理论分析的正确性，并模拟了物理现象。
The paper aims to study the numerical solution of the Zakharov-Rubenchik equations on unbounded domains, which model the propagation of two kinds of waves in plasma physics, by applying the artificial boundary method. Based on ideas of the operator splitting method and artificial boundary method of hyperbolic system and nonlinear Schrödinger equation, the artificial boundary conditions of the Zakharov-Rubenchik equations are designed on the introduced artificial boundaries to reduce the original problem defined on an unbounded domain into an initial boundary value problem on the bounded computational domain, which can be efficiently solved by finite difference method. A series of auxiliary variables is introduced to rigorously analyze the stability of the reduced initial boundary value problem through energy estimation. Numerical examples are presented to demonstrate the effectiveness of the proposed artificial boundary conditions, validate the theoretical analysis, and simulate the physical phenomena.