19. NUMERICS Namelist

19.1. Overview

The NUMERICS namelist specifies general numerical parameters not specific to any particular physics, especially those controlling the overall time stepping of the Truchas model.

19.2. DS_SOURCE Namelist Features

Required/Optional : Required

Single/Multiple Instances: Single

Cycle_Max

Description       : The maximum cycle number allowed in the given simulation, where one “cycle” corresponds to one integration time step over all physical model equations. The simulation will terminate gracefully when the cycle number reaches Cycle_Max.
Type              : integer
Default           : 1000000
Valid Values      : \((0,\infty)\)
Notes             : A simulation will also terminate gracefully if the last entry in the Output_T input variable (real) array (in the OUTPUTS namelist) is exceeded by the current simulation time t.

Cycle_Number

Description       : The cycle number to be used just prior to the first actual cycle (time step) taken in the given simulation. The first simulation cycle number is then taken to be cycle_number+ 1.
Type              : integer
Default           : 0
Valid Values      : [1, \(\infty\))
Notes             : The default value of 0 results in the first computational cycle taken to be 1. This input variable is most useful when starting simulations from a restart file that already contains a restart cycle number > 0.

Dt_Constant

Description       : A constant integration time step value to be used for all time steps in the simulation.
Physical dimension: T
Type              : real
Default           : none
Valid Values      : \((0,\infty)\)
Notes             : This Dt_Constant input variable should be used with extreme caution, as its specification overrules all other time step choices that are controlled by linear stability and accuracy considerations. In particular, NUMERICS namelist input variables Dt_Grow, Dt_Init, Dt_Max, and Dt_Min are all ignored if Dt_Constant is specified. Use of Dt_Constant is therefore advised only for controlled numerical algorithm experiments, and not for simulations intended for applications analysis and validation.

Dt_Grow

Description       : A factor to multiply the current integration time step \((\delta t)\) for the purpose of estimating the time step used during the next cycle \((\delta t_g =\) Dt_Grow \(∗\delta t)\). This candidate time step \((\delta t_g)\) is chosen only if all other currently active time step restrictions have not already limited its value below \((\delta t_g)\).
Physical dimension: dimensionless
Type              : real
Default           : 1.05
Valid Values      : [1, \(\infty\))
Notes             : Dt_Grow is ignored if Dt_Constant is specified.

Dt_Init

Description       : A Integration time step value used for the first computational cycle.
Physical dimension: T
Type              : real
Default           : \(10^{-6}\)
Valid Values      : (1, \(\infty\))
Notes             : The default value of Dt_Init is completely arbitrary, as it is always problem dependent. Unless aconstant time step is desired (via specification of Dt_Constant), then, a value for Dt_Init should be specified (instead of relying on the default) that is consistent with the time scales of interest for the simulation at hand. A general rule of thumb is to set Dt_Init smaller than the time step ultimately desired, thereby allowing the time step to grow gradually and steadily (say, over 10-20 cycles) to the desired time step value.

For restart calculations, the initial time step size is extracted from the restart file and used instead of Dt_Init, unless Ignore_Dt in the RESTART namelist has been set to true. Dt_Init is ignored if Dt_Constant is specified.

Dt_Max

Description       : Maximum allowable value for the time step
Physical dimension: T
Type              : real
Default           : 10
Valid Values      : (0, \(\infty\))
Notes             : The time step is not allowed to exceed this value, even if other accuracy- or stability-based criteria would permit it. The default value of Dt_Max is completely arbitrary, as it is always problem dependent. Unless a constant time step is desired (via specification of Dt_Constant), then, a value for Dt_Max should be specified (instead of relying on the default) that is consistent with the timescales of interest for the simulation at hand.

Dt_Max is ignored if Dt_Constant is specified.

Dt_Min

Description       : Minimum allowable value for the time step
Physical dimension: T
Type              : real
Default           : \(10^{-6}\)
Valid Values      : (0, \(\infty\))
Notes             : If the time step falls below this value, the user is informed as such and the simulation terminates gracefully. Termination occurs at this condition because is it very probable that either numerical algorithm or physical model problems have occurred and the simulation is unable to recover. The default value of Dt_Min is completely arbitrary, as it is always problem dependent. Unless a constant time step is desired (via specification of Dt_Constant), then, a value for Dt_Min should be specified (instead of relying on the default) that is consistent with the time scales of interest for the simulation at hand. A good rule of thumb to use for Dt_Min is to use a value several orders of magnitude below the time scale of interest.

Dt_Min is ignored if Dt_Constant is specified.

t

Description       : The simulation time to be used at the beginning of the first computational cycle.
Physical dimension: T
Type              : real
Default           : 0