平面域上的Bona-Smith型Boussinesq系统：理论与数值分析
Boussinesq Systems of Bona-Smith Type on Plane Domains: Theory and Numerical Analysis
AI总结：
研究二维Bona-Smith型Boussinesq系统在有界平面域上的局部适定性，并针对反射边界条件提出一种修正Galerkin方法，证明其在L²范数下达到最优收敛速率，数值实验模拟了复杂平面域中的二维表面波并比较了不同系统解。
摘要：
我们考虑一类二维Bona-Smith型Boussinesq系统，用于近似由三维Euler方程建模的表面波流动。我们证明了这些系统在有界平面域上的各种初边值问题在时间上是局部适定的。在反射边界条件的情况下，系统通过一种修正的Galerkin方法离散化，并证明该方法在$L^2$范数下以最优速率收敛。我们给出了数值实验，旨在模拟复杂平面域中具有各种初始和边界条件的二维表面波，并将Bona-Smith系统的数值解与BBM-BBM系统的类似解进行比较。
英文摘要：
We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions approximating surface wave flows modelled by the three-dimensional Euler equations. We show that various initial-boundary-value problems for these systems, posed on a bounded plane domain are well posed locally in time. In the case of reflective boundary conditions, the systems are discretized by a modified Galerkin method which is proved to converge in $L^2$ at an optimal rate. Numerical experiments are presented with the aim of simulating two-dimensional surface waves in complex plane domains with a variety of initial and boundary conditions, and comparing numerical solutions of Bona-Smith systems with analogous solutions of the BBM-BBM system.
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