Mesh Adaptation for Time Evolving Domains

              Timothy J. Baker

        MAE Dept., Princeton University
        Princeton, NJ 08540, U.S.A.


Numerous computational simulations involve a physical domain whose shape is evolving with time. Other time dependent problems involve features (e.g. vortices or shockwaves in a fluid flow) that move relative to the domain.

Mesh modification for time evolving domains can be carried out by a three stage combination of mesh movement, mesh coarsening and mesh enrichment. If the domain shape remains fixed then the last two stages, coarsening and enrichment, suffice to adapt the mesh to track time evolving features in the computed solution.

Unstructured meshes of triangles in 2D, or tetrahedra in 3D, are particularly well suited to mesh modification since local refinement and/or coarsening can be achieved without the introduction of hanging nodes or other artifices that often plague adaptation schemes for structured meshes. The mesh modification technique will be described and a number of examples will be presented to illustrate its application to the simulation of time dependent problems.