CourantNo

Description

The CourantNo function object computes the field of Courant number, i.e. Co, for time-variant simulations.

$$\text{Co} = \Delta_t \, \tau$$

where $\Delta_t$ is the time-step size, and $\tau$ is a characteristic time scale based on the local cell flow scales:

$$\tau = \frac{1}{2 V} \sum_{faces} \left| \phi_i \right|$$

Here, $V$ is the cell volume, $\phi$ the face volumetric flux, and $\sum_{faces}$ summation is over all cell faces.

The Courant number provides

• a measure of the rate at which information is transported under the influence of a flux field,
• a limiting factor for the performance of numerical schemes.

Operands

Operand	Type	Location
input	-	-
output file	-	-
output field	volScalarField	$FOAM_CASE/<time>/<outField>

Usage

Example of the CourantNo function object by using functions sub-dictionary in system/controlDict file:

Co1
{
    // Mandatory entries (unmodifiable)
    type            CourantNo;
    libs            (fieldFunctionObjects);

    // Optional entries (runtime modifiable)
    rho             rho;

    // Optional (inherited) entries
    field           <phi>;
    result          <fieldResult>;
    region          region0;
    enabled         true;
    log             true;
    timeStart       0;
    timeEnd         1000;
    executeControl  timeStep;
    executeInterval 1;
    writeControl    timeStep;
    writeInterval   1;
}

where the entries mean:

Property	Description	Type	Required	Default
type	Type name: CourantNo	word	yes	-
libs	Library name: fieldFunctionObjects	word	yes	-
rho	Name of density field	word	no	rho

The inherited entries are elaborated in:

• functionObject
• fieldExpression

Example by using the postProcess utility:

postProcess -func CourantNo

Stored properties

Fields

The Courant number is stored on the mesh database, using the default name

Co

If the field entry is set to a value other than phi, the default name becomes

Co(<field>)

This name can be overridden by using the result entry.

Further information

Tutorial:

• cavity

Source code:

• CourantNo

API:

• Foam::functionObjects::CourantNo

History: Introduced in version v1606+