Grid classification

In applied mathematics, a grid or mesh is defined as the set of smaller shapes formed after discretisation of a geometric domain.

Meshing has applications in the fields of geography, designing, computational fluid dynamics,[1] and more generally in partial differential equations numerical solving.

The shape of the elements is of great importance in solving problems in computational fluid dynamics.

Most of the fluid flow equations are easily solved by discretizing procedures using the Cartesian coordinate system.

[2] In this system the implementation of finite volume method is simpler and easier to understand.

But most of the engineering problems deal with complex geometries that don’t work well in the Cartesian coordinate system.

When the boundary region of the flow does not coincide with the coordinate lines of the structured grid then we can solve the problem by geometry approximation.

Other than this problem there is one more problem which is the cells inside the solid part of the cylinder, which are called dead cells, are not involved in the calculations so they should be removed, otherwise they would consume extra space in computer or other resources.

Therefore, there are limitation in using methods in computational fluid dynamics based on simple coordinate system (Cartesian or cylindrical) as these systems fails while modeling of complex geometries like that of an aerofoil, furnaces, gas turbine combustors, IC-engine etc.

In order to model this type of geometry we divide the flow region into various smaller sub domains.

In both these cases the domain boundaries coincide with the coordinate lines; therefore all the geometrical details can be incorporated.

There are difficulties which we face in generating the body-fitted grids in geometries like IC engine combustion chamber.

But this results in unnecessary grid resolution which leads to local variation of solution domain.

In far more complex geometries it is logical to use large number of blocks and therefore it leads to unstructured grids.

This is based on the fact since the control volume can be of any shape therefore restriction on number of adjacent cell is lifted.

In three dimension combination of tetrahedral and hexahedral elements results in hybrid grid.

Various automatic techniques especially those associated with Finite Element Method also utilize unstructured grids.