Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods, 2nd Edition

18 EMBEDDED AND IMMERSED GRID TECHNIQUES

As seen throughout the previous chapters, the numerical solution of PDEs is usually accomplished by performing a spatial and temporal discretization with subsequent solution of a large algebraic system of equations. The transition from an arbitrary surface description to a proper mesh still represents a difficult task. This is particularly so when the surface description is based on data that does not originate from CAD systems, such as data from remote sensing, medical imaging or fluid–structure interaction problems. Considering the rapid advance of computer power, together with the perceived maturity of field solvers, an automatic transition from an arbitrary surface description to a mesh becomes mandatory.

So far, we have only considered grids that are body-conforming, i.e. grids where the external mesh faces match up with the surface (body surfaces, external surfaces, etc.) of the domain. This chapter will consider the case when elements and points do not match up perfectly with the body. Solvers or methods that employ these non-body-conforming grids are known by a variety of names: embedded mesh, fictitious domain, immersed boundary, immersed body, Cartesian method, etc. The key idea is to place the computational domain inside a large mesh (typically a regular parallelepiped), with special treatment of the elements and points close to the surfaces and/or inside the bodies. If we consider the general case of moving or deforming surfaces ...