Development of immersed boundary methods for fluid flow and heat transfer

浸入边界有限元法（IB-FEM）适用于复杂几何问题。该方法将具有简单边界条件的边界符合网格的极端复杂性转化为不符合边界的简单网格，并在其上使用特殊技术强制边界条件。目前有几个问题妨碍IB-FEM成为传统方法的一种有效的、具有成本效益的替代方法。最大的挑战是开发一种通用的方法来精确实现沿边界表面的边界条件，这些边界条件不是由网格表示的，以确保IB-FEM产生与传统FEM相同的解。

The Immersed Boundary Finite Element Methods (IB-FEM) is well suited to problems involving complex geometries. The method trades the extreme complexity of a boundary conforming grid with simple boundary conditions for a simple grid that does not conform to the boundary and on which a special technique is used to enforce boundary conditions. Several issues currently prevent the IB-FEM from being an efficient cost-effective alternative to traditional approaches. The biggest challenge is the development of a general approach for accurate implementation of boundary conditions along boundary surfaces that are not represented by the mesh to ensure that the IB-FEM yields the same solution as traditional FEM.