Fluid interfaces and numercial control of waves

我的研究的第一部分是致力于开发和分析有效的数值方法，基于有限元法，用于模拟与其他类型的介质，如流体，固体或多孔介质的流体流动。用于数值计算的标准方法（利用有限元方法）是构建通常由三角形或四面体组成的网格。对于我们感兴趣的物理现象类型，当真实的域具有弯曲边界时，会出现一些数值困难。即使我们可以在计算域上构造一个尽可能接近真实的域的网格，数值计算也不一定倾向于“真实的”解。

A first part of my research is devoted to the development and the analysis of efficient numerical methods, based on the finite element method, for the simulation of fluid flows which are interfaced with other types of media such as fluid, solid or porous media. A standard approach for the numerical computations (with the finite element method) is to build a mesh generally composed of triangles or tetrahedra. For the type of physical phenomena we are interested in, some numerical difficulties arise when the real domain has curved boundaries. Even if we can construct a mesh on a computational domain as close to the real domain as desired, the numerical computations do not necessarily tend to the "real" solution.