Adaptive mesh refinement

This dynamic technique of adapting computation precision to specific requirements has been accredited to Marsha Berger, Joseph Oliger, and Phillip Colella who developed an algorithm for dynamic gridding called local adaptive mesh refinement.

In a series of papers, Marsha Berger, Joseph Oliger, and Phillip Colella developed an algorithm for dynamic gridding called local adaptive mesh refinement.

[1][2] The algorithm begins with the entire computational domain covered with a coarsely resolved base-level regular Cartesian grid.

This allows the user to solve problems that are completely intractable on a uniform grid; for example, astrophysicists have used AMR to model a collapsing giant molecular cloud core down to an effective resolution of 131,072 cells per initial cloud radius, corresponding to a resolution of 1015 cells on a uniform grid.

The advantages of a dynamic gridding scheme are: In addition, the AMR methods have been developed and applied to a wide range of fluid mechanics problems, including two-phase flows,[7] fluid-structure interactions,[8] and wave energy converters.

The image above shows the grid structure of an AMR calculation of a shock impacting an inclined slope. Each of the boxes is a grid; the more boxes it is nested within, the higher the level of refinements. As the image shows, the algorithm uses high resolution grids only at the physical locations and times where they are required.