# Time Integration Specifications¶

The first card in this section dictates whether the problem is a steady state or transient simulation. This card is required. If the steady state option is chosen, then the remaining input records are not required, as the rest of the records are used to set parameters for transient simulations, e.g., time step size, time step error control, etc. Some records are optional even for a transient simulation, as indicated below. It should be noted that the mass-matrix term multiplier in the Problem Description section (see, for example, the EQ= cards), must be set to one (1) for the transient run to evolve the fields in time. The only equations that are taken as purely quasi static are the EQ=mesh equations for the situation in which the Mesh Motion type is Arbitrary.

In addition to the transient parameter information, some Level-Set function information is also supplied to Goma in this section. The method of Level-Sets is used to track fluid-fluid or fluidsolid interfaces in an Eulerian fashion, making the problem inherently transient.

## Time Integration¶

Time integration = {steady | transient}


### Description / Usage¶

This required card is used to specify transient or steady-state calculation. Valid options are:

For a solution to the steady (time-derivative free) equations.

transient

For transient simulations.

If option steady is chosen, then none of the other Time Integration Specification cards in this section are needed.

### Examples¶

This is a sample card for a steady state simulation:

Time integration = steady


This is a sample card for a transient simulation:

Time integration = transient


## delta_t¶

delta_t = <float>


### Description / Usage¶

This card is required for transient simulations to set the value of the initial time step. The input parameter is defined as:

<float>

Any floating point number that indicates the time step in the appropriate units for your problem.

To specify a fixed time step size for an analysis, set <float> to be a negative number, e.g. -1.0e-6; the code will use a constant (positive) time step. Should convergence problems occur when a fixed step size is specified, the size of the time increment entered for the delta_t card will be reduced by half until convergence is achieved. Once a constant time step is reduced, it will not be increased.

### Examples¶

Following is a sample card for an initial time step:

delta_t = 6.e-03


If a constant time step is desired, use a negative value:

delta_t = -6.e-03


## Maximum Number of Time Steps¶

Maximum number of time steps = <integer>


### Description / Usage¶

This card sets the maximum number of time steps that may be performed for a transient simulation. Goma will stop if this limit is reached. The input parameter is defined as

<integer>

Any integer greater than zero, which will limit the number of time steps taken in a simulation.

### Examples¶

The following sample card sets the maximum number of time steps to 100:

Maximum number of time steps = 100


## Maximum Time¶

Maximum time = <float>


### Description / Usage¶

This card sets the maximum value of time that may be achieved in a transient simulation. Goma will stop if this limit is reached. The input parameter is defined as:

<float>

Any floating point number in the same units as specified in the delta_t card.

The last result written to the EXODUS II and soln.dat file in a successfully completed simulation will always be at the maximum time. This provides a cutoff time beyond which the simulation will terminate.

### Examples¶

The following sample card sets the maximum time to 105 (in units consistent with your simulation):

Maximum time = 105.


## Minimum Time Step¶

Minimum time step = <float>


### Description / Usage¶

This card sets the value of the minimum allowable time step size in a transient analysis, a useful control if the time step is being decreased due to poor convergence of the transient or iterative algorithm. The input parameter is defined as

<float>

Any floating point number in the same units as specified in the delta_t card.

### Examples¶

A sample card that sets the minimum time step to 1.e-9 follows:

Minimum time step = 1.e-9


### Technical Discussion¶

This specification provides a graceful way for the program to terminate based on the computed time step dropping below the minimum value rather than terminating by a segmentation fault or a divide-by-zero error that could result if the time step becomes too small without the benefit of this control.

## Maximum Time Step¶

Maximum time step = <float>


### Description / Usage¶

This card sets the value of the maximum allowable time step size in a transient analysis, where the input parameter is defined as

<float>

Any floating point number in the same units as specified in the delta_t card.

### Examples¶

A sample card that sets the maximum time step to 10.0 follows:

Maximum time step = 10.0


### Technical Discussion¶

This setting is useful for advection dominated simulations, such as FILL, where a Courant-like limit must be set on the value of the time step for optimal performance.

## Minimum Resolved Time Step¶

Minimum Resolved Time Step = <float>


### Description / Usage¶

Its role is to set a lower bound for the time step with respect to the Time step error tolerance. When a converged time step is obtained by GOMA, the difference between the predicted solution and final solution for that time step is compared to the Time step error tolerance. If the difference exceeds this tolerance the step fails and the time step is cut (usually by a factor of 2), UNLESS the time step falls below the Minimum Resolved Time Step size. In this case the step is accepted, even if this error tolerance is not achieved. This provides a mechanism for the modeler to control what phenomena is resolved and what phenomena is ignored.

<float>

Any floating point number in the same units as specified in the delta_t card.

### Examples¶

A sample card that sets the maximum time step to 10.0 follows:

Maximum Resolved Time Step = 10.0


### Technical Discussion¶

See GT-034 for a thorough discussion.