The term discretisation means approximation of a problem into discrete quantities.
The FV method and others, such as the finite element and finite difference
methods, all discretise the problem as follows:
Spatial discretisation
Defining the solution domain by a set of points that
fill and bound a region of space when connected;
Temporal discretisation
(For transient problems) dividing the time
domain into into a finite number of time intervals, or steps;
Equation discretisation
Generating a system of algebraic equations in
terms of discrete quantities defined at specific locations in the domain,
from the PDEs that characterise the problem.
OpenFOAM frequently needs to store sets of data and perform functions, such as
mathematical operations, on the data. OpenFOAM therefore provides an array
template class List<Type>, making it possible to create a list of any object of class
Type that inherits the functions of the Type. For example a List of vector is
List<vector>.
Lists of the tensor classes are defined as standard in OpenFOAM by the template
class Field<Type>. For better code legibility, all instances of Field<Type>, e.g.Field<vector>, are renamed using typedef declarations as scalarField, vectorField,
tensorField, symmTensorField, tensorThirdField and symmTensorThirdField.
Algebraic operations can be performed between Fields subject to obvious
restrictions such as the fields having the same number of elements. OpenFOAM also
supports operations between a field and single tensor, e.g. all values of a
Field U can be multiplied by the scalar 2 with the operation U = 2.0 *U.
