二维Boussinesq-全频散系统模拟内波传播的数值方法
A numerical method for two-dimensional Boussinesq-Full Dispersion systems modelling internal wave propagation
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中文总结 AI 辅助
本文提出一种基于谱Fourier-Galerkin方法和隐式中点规则的数值方法，用于求解二维内波传播的Boussinesq-全频散模型，并分析其收敛性与性能。
中文摘要 AI 辅助
本文关注二维渐近模型的数值逼近，这些模型以界面偏差和速度的偏微分方程形式描述两层系统中内波的传播。在研究了周期初值问题的适定性之后，分析了基于谱Fourier-Galerkin方法的半离散逼近的收敛性。随后，利用隐式中点规则对所得半离散系统进行时间上的数值积分。描述了全离散格式的一些性质，并通过一些数值实验展示了其性能。
英文摘要
The paper is concerned with the numerical approximation of some two-dimensional asymptotic models for the propagation of internal waves in a two-layer system in the form of pde's for the interfacial deviation and the velocity. After the study of well-posedness of the periodic initial-value problem, the convergence of a semidiscrete approximation based on a spectral Fourier-Galerkin method is analyzed. The resulting semidiscrete system is then integrated numerically in time with the implicit midpoint rule. Some properties of the fully discrete scheme are described and its performance is illustrated with some numerical experiments.
发表机构
- University of Valladolid（巴利亚多利德大学）
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