Mesh resolution can determine how good of a solution your model will provide. Too little resolution and you are not solving the intended equations. Too much resolution and you are wasting time and computational space. The typical numerical modeling process includes a mesh resolution study in which the mesh is resolved until no more changes are seen in the results.
For example, the meshes below show four levels of resolution. An initial concentration cloud is applied and advected through the domain from left to right. The results at a single instant in time are shown for each of the meshes. The results are obviously different. However, the results for the refined mesh #2 and #3 are very similar. This indicates that the refined mesh #2 is likely enough resolution to determine the location of maximum concentration and time of arrival of the concentration.
The adaption feature in AdH that allows the mesh to refine during the simulation based on user supplied inputs. The user provides a tolerance value that when the residual error becomes larger than this value, an element can be split, up to a specified maximum level. The equation below is the residual error calculation.
Once the added resolution is no longer needed, it is removed from the mesh. This is a good feature for a moving front such as dye clouds, salinity intrusion, supercritical flow, vessel movement, and sediment transport that move spatially and in time, as well as the standard hydraulic features that require additional resolution.