Template:Gravity Waves Time Step

Gravity Waves Time Step

The time step tool is intended to assist in the selection of a time step for a numerical simulation that is based on the Courant number calculation. This tool can be thought of as the inverse of the Gravity Courant Number tool. Refer to that documentation of the Gravity Courant Number tool for clarification. The objective of this tool is to compute the time step that would result in the specified Courant number for the given mesh and velocity field. The user would then select a time step for analysis that is at least as large as the maximum value in the resulting times step dataset.

Note: the variable here is depth, not elevation. For applications relative to mean sea level, using the negative of the elevation relative to a datum is acceptable, but if the water level will vary, the depth is actually the water level minus the ground elevation

${\displaystyle TimeStep=CourantNumber*NodalSpacing/(Gravity*Depth)^{0.5}}$

Typically, the Courant number specified for this computation is <= 1.0 for Courant limited solvers. Some solvers maintain stability for Courant numbers up to 2 or some solver specific threshold. Specifying a Courant number below the maximum threshold can increase stability since the computation is approximate.

The Gravity Waves Time Step tool dialog has the following options:

Input Parameters

• Input dataset – Specify the elevation dataset (or depth dataset if using depth option).
• Input dataset is depth – Specify Specify if the input dataset is depth.
• Gravity – Enter the gravity value.
• Use courant number – Enter the Courant number.

Output Parameters

• Gravity waves time step dataset – Enter the name for the new gravity wave time step dataset.

Related Topics

• Advective Time Step
• Gravity Waves Courant Number