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The Courant number is a spatially varied (dataset) dimensionless value representing the time a particle stays in a cell of a mesh/grid. This is based on the size of the element and the speed of that particle. A Courant number of 1.0 implies that a particle(parcel or drop of water) would take one time step to flow through the element. Since cells/elements are not guaranteed to align with the flow field, this number is an approximation. This dataset is computed at nodes so it is uses the average size of the cells/elements attached to the node. (If the future we could have a cell based tool that computes the Courant number for the cell, but this is still an approximate number based on the direction.)

The advective courant number makes use of a velocity dataset that represents the velocity magnitude field on the desired geometry. The tool computes the Courant number at each node in the selected geometry based on the specified time step.

${\displaystyle {\displaystyle CourantNumber=TimeStep*Velocity/NodalSpacing}}$

If the input velocity magnitude dataset is transient, the resulting ${\displaystyle {\displaystyle CourantNumber}}$ dataset will also be transient.

For numerical solvers that are Courant limited/controlled, any violation of the Courant condition, where the Courant number exceeds the allowable threshold could result in instability. Therefore, the maximum of the Courant number dataset gives an indication of the stability of this mesh for the specified time step parameter.

This tool is intended to assist with numerical engine stability, and possibly the selection of an appropriate time step size.

#### Input Parameters

• Input dataset – Specify which velocity dataset will be used to represent particle velocity magnitude.
• Use timestep – Enter the computational time step value.

#### Output Parameters

• Advective courant number dataset – Enter the name for the new dataset which will represent the Courant number. (Suggestion: specify a name that references the input. Typically this would include the time step used in the calculation. The velocity dataset used could be referenced. The geometry is not necessary because the dataset resides on that geometry.)