Useful Numbers
Courant Number

There is a very especific relation between the finite differences in space and time. Logically they are related by a velocity. The critical case is the maximum velocity and the minimum space (given by the geometry of the grid). The reciprocal of the relation between these two values gives the maximum allowed differential in time. The Courant number is defined as the differential time times the characteristic velocity divided by the characteristic space. This number must be always lower than one to get convergence.

Reynolds Number

The Reynolds Number relates the characteristic distance and velocity of the flow with the kinematic viscosity. For higher Reynolds Numbers the flow goes to turbulent and for smaller tends to be laminar.

Dimensions in ParaFOAM

Based in a SI units convention: [kg m s K mol A cd]. For example the kinematic viscosity units (m*m/s) are represented by [0 2 -1 0 0 0 0].


The grid is constructed with a primary division in blocks. Each block-corner defines a vertice. Each block is divided in X, Y and Z directions according either with a uniform or non-uniform cell division.

It is very important to name the whole mesh vertices, blocks and walls with complete coherence.


To give names to the vertices, put the origen in the intersection of the left, lower and rear walls, and align X horizontally to the right, Y vertically to the top and Z horizontally to the front.

The origen will be called the 0 vertice. The vertice number 1 will be the next in the X direction and so on until reach the right end. The count continues moving Y to the next level and from the left to the right as before. Once the top right point is reached in the rear wall, continue counting in the same order over the next wall. The last vertice should be the one in the intersection of the front, top and right walls.


To name the blocks follow the same order given for the vertices. It is a priority in the X direction, after in the Y direction and finally in the Z direction. The count begins in 0 again.


Each block has six walls, but there is not necessity to define all of them because some are only a block division and not a boundary for the whole problem. The name for a wall is given by the secuencial vertice names, beginning with the lower value vertice and in a clockwise rotation direction when viewing from the interior of the corresponding block.

The type of the wall will define some boundary conditions to the problem.

Some of the most relevant values used as parameters to control the fluid simulation are related to the time in different ways.

deltaT is the interval of time equal or lower thant the one calculated by using the Courant Number.

time step is set by the writeInterval value and specify the number of deltaT steps which have to pass each time the computer records the complete fields results.

startTime and endTime can be set in different ways. For example startTime as 5 implies the initial time 5s and startTime can also be different according with the startFrom set (i.e. latestTime).

An important characteristic in OpenFOAM is that the problem can be solved with one mesh and the results can be adjusted again over the last obtained but using a fine mesh.

The complete U and P field information is stored for each time with a simple well organized way. All the initial data, like the grid or geometry, physical properties, boundary conditions and root address are stored in files called dictionaries (i.e. ControlDict).