A type of → algorithm that dynamically achieves high
→ resolution in localized regions of multidimensional
→ numerical simulations.
AMR provides a higher → accuracy solution at
lower costs, through an automatically → optimal
distribution of → grid points for the
computation region. It relies on locally refined mesh or mesh
patches to increase the resolution of an underlying
coarse mesh only where needed.
It can alleviate some of the complexities of the generation of high
quality grid and reduce the number of → iterations of
"trial-and-error" between the grid generation and solution
required for tailoring the grid to the specification of a
problem. Thus, it can offer orders of magnitude saving in
computational and storage costs over an equivalent uniformly refined
mesh. AMR was originally developed for → inviscid,
→ compressible flow (Berger et al., 1984,
Adaptive Mesh Refinement for Hyperbolic Partial Differential
Equations. J. Comp. Phy., 53, 484). It
has been extended to solve → Navier-Stokes equations,
time dependent problems and more. Several
AMR techniques have been developed and applied to compressible flow fields to capture
characteristics at the strong gradient or discontinuous regions requiring higher space resolution,
such as regions involving → shock waves,
vortices (→ vortex), and
→ wakes
(see, e.g., Qingluan Xue, "Development of Adaptive Mesh Refinement Scheme and
Conjugate Heat Transfer Model for Engine Simulations" (2009), Iowa State Univ., Graduate
Theses and Dissertations, Paper 10678).
See also → Smoothed Particle Hydrodynamics.

1) Fineness or elegance of feeling, taste, manners, language, etc.
2) The act or process of refining. the quality or state of being refined.
3) An improved, higher, or extreme form of something. Math.: A → set whose elements include the elements
of a given set (Dictionary.com).