AMR Terminology
- Base Grid : Initial griding of the
computational domain, typically a uniform “coarse” mesh with minimum
required resolution.
- Grid Hierarchy : Hierarchical grid
structure with multiple levels of grid resolution.
- Time Integration : Solving the PDE
on the grid to take one timestep.
- Local Truncation Error (LTE) :
Locally computed error in the PDE solution. Used to identify grid points
requiring refinement.
- Refinement : Addition of finer
resolution grids in regions with high LTE. Refinement is performed both in time
and space.
- Regriding : Creating the new grid
hierarchy, adding high-resolution grids in refined regions and removing
high-resolution grids no longer required. The regriding process includes the
initialization of refined grids.
- Clustering : Combining grid points
with high LTE into regular regions to be refined.
- Prolongation : Transfer of
information from a coarser grid to a finer grid. Prolongation is used to
initialize higher resolution grids on creation.
- Restriction : Transfer of
information from finer grids to coarser grid. Restriction is performed every
timestep to ensure that the solutions on the fine and coarse grids do not
diverge.