geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, a corner-point grid is a

tessellation A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional ...

of a Euclidean 3D volume where the base cell has 6 faces ( hexahedron). A set of straight lines defined by their end points define the ''pillars'' of the corner-point grid. The pillars have a lexicographical ordering that determines neighbouring pillars. On each pillar, a constant number of nodes (corner-points) is defined. A corner-point cell is now the volume between 4 neighbouring pillars and two neighbouring points on each pillar. Each cell can be identified by integer coordinates

(i,j,k)

, where the

k

coordinate runs along the pillars, and

i

and

j

span each layer. The cells are ordered naturally, where the index

i

runs the fastest and

k

the slowest. Data within the interior of such cells can be computed by trilinear interpolation from the boundary values at the 8 corners, 12 edges, and 6 faces. In the special case of all pillars being vertical, the top and bottom face of each corner-point cell are described by bilinear surfaces and the side faces are

plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * Planes (gen ...

s. Corner-point grids are supported by most

reservoir simulation Reservoir simulation is an area of reservoir engineering in which computer models are used to predict the flow of fluids (typically, oil, water, and gas) through porous media. The creation of models of oil fields and the implementation of ca ...

software, and has become an industry standard.

Degeneracy

A main feature of the format is the ability to define erosion surfaces in

geological modelling Geologic modelling, geological modelling or geomodelling is the applied science of creating computerized representations of portions of the Earth's crust based on geophysical and geological observations made on and below the Earth surface. A g ...

, effectively done by collapsing nodes along each pillar. This means that the corner-point cells degenerate and may have less than 6 faces. For the corner-point grids non-neighboring connections are supported, meaning that grid cells that are not neighboring in ijk-space can be defined as neighboring. This feature allows for representation of faults with significant throw/displacement. Moreover, the neighboring grid cells do not need to have matching cell faces (just overlap).

References

Corner Point Grid
''Open Porous Media Initiative'' * Aarnes J, Krogstad S and Lie KA (2006)
Multiscale Mixed/Mimetic Methods on Corner Point Grids
''SINTEF ICT, Dept. Applied Mathematics'' Tessellation Geometry {{geometry-stub