Card 2b - Analyzer Control (transient runs)

GRADNT

GRADNT = -2 uses the explicit exponential forward differencing integration technique. The temperature of an element at time t + dt is calculated from the temperatures, heat loads, and conductance values at time t. At time t, the equilibrium temperature T_eq and the RC value for each element are calculated, where RC is the element's capacitance divided by the sum of its conductances. The exponential forward differencing technique is unconditionally stable for all values of dt but does not conserve the energy of the system, which may lead to erroneous results with dt >> RC_MIN, where RC_MIN is the smallest non-zero RC value in the model. Performance of the algorithm is degraded if zero capacitance elements are present, as the temperatures of zero-capacitance elements are calculated iteratively at each integration time step. The new temperature T(t + dt) is calculated by:

GRADNT = -3 uses the explicit forward differencing integration technique. The forward differencing technique is first-order accurate and conserves the energy of the system but may become unstable if dt > RC_MIN. It is recommended to set DT = 0 when using this option, although this may result in very small integration time steps and excessively long runs. Since this method is explicit (no iterations are performed) for models containing only non-zero capacitance elements, it is quite efficient if a reasonable integration time step can be specified. Temperatures of zero-capacitance elements are calculated iteratively at each integration time step, resulting in slower runs.

GRADNT = -4 uses the implicit forward–backward or Crank–Nicolson technique:
where RC is the time constant of the element. T(t + dt) is calculated iteratively because Teq(t + dt) needs to be estimated at each time step. The default maximum number of iterations is 100, which can be changed on a Card 9 PARAM NLOOP Card. The temperature convergence criterion defaults to .001, but this may be overridden with a Card 9 PARAM TDIFS Card. A warning message is issued if the maximum number of iterations is exceeded. This method is unconditionally stable for all values of dt. Choosing a reasonable integration time step dt is crucial. If DT = 0, the integration time step defaults to RCMIN/2, generally too small, yielding long runs. Large integration time steps may result in inaccuracies and lack of convergence. It is best to specify dt = DT explicitly, typically as the largest time interval where each element's temperature rise can be safely considered linear.
GRADNT = -5 uses the implicit variable α method:
where α is the degree of implicitness of the method. α defaults to 1 (backward differencing technique) but may be specified at any value with a Card 9 PARAM ALPHA. For α = 0 this defaults to the forward differencing technique, and for α = 5 to the forward-backward differencing technique. For large integration time steps the default backward differencing technique generally yields more accurate results than the Crank-Nicolson technique. Otherwise, the same rules apply to specifying DT. This is the recommended integration algorithm. where: α is the degree of implicitness of the method.α defaults to 1 (backward differencing technique) but may be specified at any value with a Card 9 PARAM ALPHA.
GRADNT = -6 uses the fully implicit integration method, similar to the implicit variable α method (GRADNT = -5), except that all heat loads, capacitances, and conductances are updated in every iteration of the nonlinear solve loop of the transient run.
GRADNT = -9 does not run the Analyzer.

TABS

TABS is the temperature of absolute zero. It is used to evaluate radiative conductances and air densities for hydraulic elements. It can be greater than 0 or less than 0, e.g., ±273 or ±460.

DTP

DTP is the elapsed time between printouts.

DTP = 0 results in a single printout at the end of the run. DTP can be interpolated from tables (see Card 9 - INTERP Analyzer Table Interpolation, Card 9 - TABTYPE Table Variable Type Definition, and Card 9 - TABDATA Analyzer Table Data) or defined in a user-written subroutine.
DTP < 0 results in occurring a printout every DTP'th time step.

DT

DT specifies the integration time step parameter dt. DT can be interpolated from tables see Card 9 - INTERP Analyzer Table Interpolation, Card 9 - TABTYPE Table Variable Type Definition, and Card 9 - TABDATA Analyzer Table Data or defined in a user-written subroutine.

DT = 0 defaults the integration time step to RC_MIN/2.
DT > RC_min results that the solution may become unstable with the forward differencing technique.
DT < RC_min sets the integration time step to |DT| RC_MIN/2, constant multiple of RC_MIN.

TST

TST is the starting time of a transient run.

TF

TF is the final time of the run.

TRDMP

TRDMP is the transient iteration damping parameter, equivalent to DT of steady–state runs. TRDMP = blank defaults to 1.0.

Code example

-3 -273 10 0 0 20 $ TRANSIENT RUN, FORWARD DIFFERENCING PRINTOUT
 $ EVERY 10 UNITS. TOTAL TIME = 20 UNITS,
 $ INTEGRATION TIME STEP = 20 UNITS.

Notes

For more information, see Analyzer module. For more information on table interpolation and other analyzer options, see Card 9.

Temperatures are written on TEMPF file at each DTP printout interval.

Initial temperatures default to zero, unless specified by Card 9 TINIT or if a file TEMPF is present at the start of a run, in which case the set of temperatures whose time value is closest to the TST parameter are used as the starting temperatures. This is useful for restarting steady–state runs that have not completely converged. TINIT Cards override temperatures specified in a TEMPF file.
Temperature printouts are specified with Card 9 PRINT.
Temperature boundary conditions are specified with Card 9 SINK. Heat load boundary conditions may be calculated from geometry (orbital heat loads), or specified with Card 9 QNODE. Both temperature and heat load boundary conditions may be specified to be table-dependent with Card 9 INTERP or varied in a user-written subroutine.