Adaptive mesh refinement

Adaptive mesh refinement (AMR) dynamically increases the resolution of a computational mesh in regions where estimated numerical error or physical detail demands it.

A posteriori error estimation: Methods that estimate the error in a numerical solution after computing it. AMR uses these estimates to decide where additional resolution is needed.
Computational mesh: A partition of a computational domain into cells, elements, or other discrete units. AMR changes this spatial partition while representing the same domain.
Computational fluid dynamics: The numerical simulation of fluid flow using discretized governing equations. AMR concentrates cells around shocks, vortices, and boundary layers.
Uniform grid: A computational grid whose cells have the same spacing throughout its domain. Uniform grids avoid AMR’s changing resolution and complex refinement interfaces.
Parallel computing: The use of multiple processors to perform parts of a computation simultaneously. AMR requires refined patches to be distributed and rebalanced across processors.
Mesh refinement: The process of subdividing elements in a computational mesh to increase spatial resolution. AMR automates this process selectively rather than refining the entire mesh.
Discretization: The conversion of continuous equations or domains into finite numerical representations. AMR adapts the discrete representation used to approximate the underlying equations.
Shock wave: A thin moving discontinuity in a fluid’s pressure, density, or velocity. Resolving a shock requires dense cells only near its narrow front.
Unstructured mesh: A mesh whose elements have no fixed regular pattern of connectivity or shape. Unstructured meshes adapt through flexible element placement rather than necessarily using AMR’s hierarchy.
Load balancing: The distribution of computational work among processors to avoid idle resources. Unevenly distributed refinement can leave processors with very different workloads.

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