Development of immersed boundary methods for fluid flow and heat transfer

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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.