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

13 INTERPOLATION

The need to interpolate quickly fields of unknowns from one mesh to another is common to many areas of CFD and, more generally, to computational mechanics and computational physics. The following classes of problems require fast interpolation algorithms.

(a) Simulations that require different grids as the solution proceeds. Examples of this kind are adaptive remeshing for steady-state and transient simulations (Löhner and Ambrosiano (1990), Peraire et al. (1992b), Weatherill et al. (1993b)), as well as simple remeshing for problems where grid distortion due to movement becomes too severe (Baum and Löhner (1993), Mestreau et al. (1993), Löhner et al. (1999)).

(b) Simulations with overlapping grids. The key idea here is to simplify the mesh generation process and to avoid the regeneration of grids for problems with moving bodies by generating for each component (e.g., wing, pylon, tail, engine inlet, etc.) a local, independent grid. These independent grids overlap in certain regions. The solution to the global problem is obtained by interpolating between the grids after each timestep (Benek et al. (1985), Dougherty and Kuan (1989), Meakin and Suhs (1989), Meakin (1993, 1997), Rogers et al. (1998), Nakahashi et al. (1999)).

(c) Loose coupling of different codes for multi-disciplinary applications. In this case, if any of the codes in question are allowed to perform adaptive mesh refinement, the worst-case scenario requires a new interpolation problem at every timestep ...