Adaptive gridding techniques fall into
two broad classes, adaptive mesh redistribution (i.e.
Movind Mesh Method) and adaptive mesh refinement, both
contained in the acronym AMR. Techniques for the moving
mesh method continuously reposition *a fixed number*
of cells, and so they improve the resolution in particular
locations of the computational domain.

It has been amply demonstrated that significant
improvements in accuracy and efficiency can be gained
by using the moving mesh methods for problems having large
solution variations. This is especially true in areas
such as fluid dynamics, hydraulics, combustion, and heat
transfer. For problems in these areas, very fine meshes
are often required over a small portion of the physical
domain to resolve large solution variations there. Numerical
solution of these problems using uniform meshes is formidable,
even with the use of supercomputers when the systems involve
two or more spatial dimensions. Because of the great potential
of the moving mesh methods for reducing computational
costs and data storages without reducing the overall level
of accuracy, it is a forefront area in scientific computation.