二维Boussinesq系统的FreeFem++求解：平坦底床情形
Solution of 2D Boussinesq systems with FreeFem++: The flat bottom case
AI总结：
本文使用FreeFem++和P1有限元空间离散及二阶龙格-库塔时间格式，数值求解二维Boussinesq系统，并通过网格自适应技术优化算法，结果与文献一致。
摘要：
我们考虑二维空间中的不同Boussinesq系统族。这些系统近似三维欧拉方程，由三个耦合的非线性色散波动方程组成，描述理想流体在水平底床上小振幅长表面波的传播。我们提出了一个FreeFem++代码，旨在数值求解这些系统，其中采用P1有限元进行空间离散，时间上使用二阶龙格-库塔格式。我们详细介绍了代码，并使用了网格自适应技术。对所采用的算法进行了优化，并对不同Boussinesq族的解进行了比较。我们获得的结果与文献中的结果一致。
英文摘要：
We consider here different family of Boussinesq systems in two space dimensions. These systems approximate the three-dimensional Euler equations and consist of three coupled nonlinear dispersive wave equations that describe propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. We present here a FreeFem++ code aimed at solving numerically these systems where a discretization using P1 finite element for these systems was taken in space and a second order Runge-Kutta scheme in time. We give the detail of our code where we use a mesh adaptation technique. An optimization of the used algorithm is done and a comparison of the solution for different Boussinesq family is done too. The results we obtained agree with those of the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
