# TIME_SEQUENCE

Specifies the time stepping and staggering strategy.

## Type

AcuSolve Command

## Syntax

TIME_SEQUENCE {parameters}

## Qualifier

This command has no qualifier.

## Parameters

- min_cases >=0 [=1]
- Minimum number of optimization cases allowed for the run.
- max_cases >=0 [=50]
- Maximum number of optimization cases allowed for the run.
- optimization_convergence_tolerance >=0 [=1.e-4]
- A necessary condition for the termination of an optimization run is that all convergence measures must be less than this tolerance.
- final_time (real) >=0 [=0]
- Final time of the run. The run will terminate when the analysis time reaches the final time. The run may terminate earlier due to other criteria. If zero, this option is ignored.
- min_time_steps or min_steps (integer) >=0 [=1]
- Minimum number of time steps before terminating a run due to convergence to steady state, or ending a case if multiple cases are used in a run.
- max_time_steps or max_steps (integer) >=0 [=1]
- Maximum number of time steps allowed for a run or a case. The run may terminate, or the case may end, earlier due to other criteria. If zero, this option is ignored.
- initial_case_time_steps (integer) >=0 [=0]
- Minimum number of time steps used for the initial case. This option will also override the max_time_steps parameter for the initial case. If zero, this option is ignored.
- convergence_tolerance or conv_tol (real) >=0 [=1.e-4]
- Steady-state convergence tolerance. The run will terminate if all convergence measures within a time step are less than this tolerance. This criteria requires that at least min_time_steps time steps are solved and that termination_delay consecutive time steps have passed while satisfying the convergence tolerance.
- termination_delay or exit_delay (integer) >=0 [=0]
- Minimum number of consecutive time steps in which the steady-state convergence criteria must be satisfied before terminating the run. A value of zero results in the same behavior as one.
- lhs_update_initial_times or lhs_init_steps (integer) >=0 [=1]
- The number of initial time steps in which the left-hand-side (LHS) matrices of all staggers are discarded at the start of every time step.
- lhs_update_frequency or lhs_freq (integer) >=0 [=0]
- The time step frequency at which the left-hand-side (LHS) matrices of all staggers are discarded at the start of such time steps. If zero, this option is ignored.
- min_stagger_iterations or min_stg_iters (integer) >=0 [=1]
- Minimum number of stagger iterations before advancing to the next time step. If zero, this option is ignored.
- max_stagger_iterations or max_stg_iters (integer) >=0 [=1]
- Maximum number of stagger iterations before advancing to the next time step.
- stagger_convergence_tolerance or stg_conv_tol (real) >=0 [=1.e-4]
- Time step convergence tolerance. The stagger iteration is terminated when all convergence measures within the stagger iteration are less than this convergence tolerance and at least min_stagger_iterations has been solved.
- stagger_lhs_update_frequency or stg_lhs_freq (integer) >=0 [=0]
- The stagger iteration frequency at which the left-hand-side (LHS) matrices of all staggers are discarded at the start of such staggers. If zero, this option is ignored.
- staggers or stgs (list) [no default]
- List of staggers to be executed. Staggers are solved in the specified sequence.
- allow_stagger_reordering or stg_reorder (boolean) [=off]
- Allow AcuSolve to change the stagger order to optimize solution stability.

## Description

This command specifies the time stepping and stagger iteration strategy and parameters.

```
Loop over time steps
Predict all active solution fields
Loop over staggers
Stagger 1:
Loop over nonlinear iterations
Form stagger residual and if needed LHS matrix
Solve linear equation system
Update stagger solution field(s)
Check nonlinear convergence
End nonlinear loop
...
Stagger N:
Loop over nonlinear iterations
Form stagger residual and if needed LHS matrix
Solve linear equation system
Update stagger solution field(s)
Check nonlinear convergence
End nonlinear loop
Check stagger convergence
End stagger loop
Check time step convergence
Optionally compute and output results
Determine time increment of the next time step
End time step loop
```

The loops over the time steps and staggers and the sequence of staggers are controlled by the TIME_SEQUENCE command. The loop over each stagger's nonlinear iterations, formations, and solution of stagger equations is controlled by the STAGGER command. The selection of the time increments is controlled by the TIME_INCREMENT command. The predictor multi-corrector parameters are controlled by the TIME_INTEGRATION command. Convergence checking parameters that are common to all staggers are set in the CONVERGENCE_CHECK_PARAMETERS command. Linear solver parameters that are common to all staggers are set in the LINEAR_SOLVER_PARAMETERS command.

- Analysis time exceeds the final_time.
- max_time_steps time steps are solved.
- All convergence measures of the last termination_delay+1 time steps are below the convergence_tolerance and a minimum of min_time_steps time steps is solved.
- User signals termination.
- A fatal error occurs.

- max_stagger_iterations stagger iterations are performed.
- min_stagger_iterations stagger iterations are performed and the last set of convergence measures fall below stagger_convergence_tolerance.

```
TIME_SEQUENCE {
staggers = { "flow", "turb", "temp" }
...
}
STAGGER( "flow" ) {
equation = flow
...
}
STAGGER( "temp" ) {
equation = temperature
...
}
STAGGER( "turb" ) {
equation = turbulence
...
}
```

```
TIME_SEQUENCE {
staggers = { "flow", "turb", "flow","temp" }
...
}
```

solves the "flow" stagger before and after the "turb" stagger.

```
TIME_SEQUENCE {
lhs_update_initial_times = 10
lhs_update_frequency = 6
stagger_lhs_update_frequency = 3
min_stagger_iterations = 1
max_stagger_iterations = 3
}
```

the LHS matrices are discarded at the beginning of the first 10 time steps, plus every 6 time steps starting from time step six. In addition, a minimum of one and a maximum of three stagger iterations are performed per time step. If iteration three is required, then the LHS matrices are discarded prior to this iteration.

Convergence checks are performed on the residual and solution increments. For the residual, the norm of the residual is normalized with respect to the norm of the forces making up the residual. This ratio is the relevant measure, because it measures the ratio of the out-of-balance forces to the value of the forces. This ratio is computed separately for each solution field. For the solution increment, the norm of the solution increment is normalized with respect to the norm of the solution field prior to updating the solution. This ratio is also computed separately for each solution field. These ratios are used to check for convergence. Convergence occurs when all residual and solution increment ratios fall below the specified tolerance. The CONVERGENCE_CHECK_PARAMETERS command may be used to control the relative importance of each ratio.

```
TIME_SEQUENCE {
final_time = 0
min_time_steps = 0
max_time_steps = 100
convergence_tolerance = 1.e-3
termination_delay = 0
lhs_update_initial_times = 0
lhs_update_frequency = 1
min_stagger_iterations = 1
max_stagger_iterations = 1
stagger_convergence_tolerance = 1.0
stagger_lhs_update_frequency = 0
staggers = { "flow", "turb", "temp", "spec1" }
}
STAGGER( "flow" ) {
equation = flow
min_stagger_iterations =1
max_stagger_iterations =1
...
}
...
```

```
TIME_SEQUENCE {
final_time = 1800
min_time_steps = 0
max_time_steps = 100
convergence_tolerance = 0.0
termination_delay = 0
lhs_update_initial_times = 0
lhs_update_frequency = 1
min_stagger_iterations = 2
max_stagger_iterations = 2
stagger_convergence_tolerance = 1.0
stagger_lhs_update_frequency = 1
staggers = { "flow", "turb", "temp", "spec1" }
}
STAGGER( "flow" ) {
equation = flow
min_stagger_iterations = 1
max_stagger_iterations = 1
...
}
...
```

```
TIME_SEQUENCE {
final_time = 1800
min_time_steps = 0
max_time_steps = 100
convergence_tolerance = 0.0
termination_delay = 0
lhs_update_initial_times = 0
lhs_update_frequency = 1
min_stagger_iterations = 1
max_stagger_iterations = 4
stagger_convergence_tolerance = 1.e-3
stagger_lhs_update_frequency = 1
staggers = { "flow", "turb", "temp","spec1" }
}
STAGGER( "flow" ) {
equation = flow
min_stagger_iterations = 1
max_stagger_iterations = 2
convergence_tolerance = 1.e-3
...
}
...
```

```
TIME_SEQUENCE {
...
staggers = { "abaqus", "flow", "turb", "temp", "spec1" }
}
STAGGER( "abaqus" ) {
equation = external_code
...
}
```

See the EXTERNAL_CODE command for details on DC-FSI problems.

```
TIME_SEQUENCE {
...
staggers = { "flow", "particle" }
}
STAGGER( "particle" ) {
equation = particle
}
```

For some applications, the order in which the staggers are solved can have a significant impact on the stability of the simulation. For example, applications involving fluid-structure interaction benefit from solving the mesh stagger first. However, for applications involving free surfaces, the flow equations should be solved first. The allow_stagger_reordering option lets AcuSolve override the stagger order that you specified to create a stagger order with optimal stability for the given application. This parameter only has an impact on the behavior of the solver when a moving mesh simulation is performed.

```
TIME_SEQUENCE {
staggers = { "flow", "turb", "mesh" }
allow_stagger_reordering = on
...
}
```

If allow_stagger_reordering=on, AcuSolve will first check to see if the mesh equation is active. If it is, it then checks to see if there are any free surface boundary conditions present in the simulation. If free surfaces exist, the stagger sequence is ordered such that the flow stagger is solved first. If no free surfaces are present, then the stagger sequence is ordered such that the mesh stagger is solved first. Note that the default solution strategy created by the AUTO_SOLUTION_STRATEGY command will set this option to off unless mesh=arbitrary_lagrangian_eulerian.