Synopsis of the Transient solvers in ESATAN.

1. SLFWBK

This routine performs transient thermal analysis by implicit forward-backward differencing—the Crank-Nicolson method. EXPLAIN THE CRANK NICOLSON METHODThe user is required to specify the following control constants: the time step length(DTIMEI); the problem start time (TIMEO) if this is not 0.0; the problem end time(TIMEND); the output interval (OUTINT); the maximum iteration count (NLOOP)for each time step; the relaxation criterion (RELXCA) for convergence on a timestep.The time step length is taken as the user supplied initial time step length, DTIMEI, unless the control constant DTPMAX has been set. DTPMAX specifies the maximum temperature change allowable over a time step.The program increases the time step to bring the maximum temperature change in line with the user supplied maximum. If DTPMAX is exceeded then the time step is reduced and the temperatures recalculated. If DTPMAX has been set to regulate the time step length then it is advisable that DTMAX and DTMIN are set. DTMAX and DTMIN specify the maximum and minimum time step lengths allowable. Where DTPMAX would lead to a smaller time step, DTMIN is used and the solution continues but an error code is set. The change in temperature at each node may be damped via the control constant DAMPT.The user can specify the type of units used by setting the control constants STEFAN and TABS.$VARIABLES1 is executed at the start of each time step and $VARIABLES2 at the end. $OUTPUTS is executed at the beginning of the transient, every OUTINT units of time during the transient and on completion of the transient.

Restrictions:This routine can only be used with pure thermal models. Control constantsDTIMEI, TIMEND, NLOOP and RELXCA must be specified. It requires 3*NNTlocations of dynamic core (NNT = total number of nodes in system). SLFWBKmay be called from the $EXECUTION block only.

2. SLCRNC

SLCRNC performs the transient by calculating the rate of change of temperature ofeach node at the beginning and end of the time step, and using the average topredict the end of time step temperatures (the change in temperature of a nodebeing the average rate of change multiplied by the time step length). The variationin the rate of change of temperature over time is an important indicator ofacceptable time step length, and hence DTROCA specifies the limit on themaximum change in the rate of change of temperature over a time step multipliedby the time step length. In most circumstances a value of between 1.0 and 10.0 forDTROCA is appropriate.

3. SLGEAR and SLGRDJ

These routines perform transient thermal analysis by backwards differencing usingthe Gear formulation. The time step length is dynamically optimised by the solverafter using an initial value of CSGMIN.The user is required to specify the following control constants; the problem starttime (TIMEO) if this is not equal to 0.0; the problem end time (TIMEND); theoutput interval (OUTINT); the maximum iteration count (NLOOP) for each timestep and the relaxation criterion (RELXCA) used to check convergence and tochoose time step length and solution order. The control constants DTMIN andDTMAX may also be set to specify the minimum and maximum time stepsallowed.The user can specify the type of units used by setting the control constantsSTEFAN and TABS.The Gear formulation consists of a prediction followed by an iterated correctorstage for each time step. This corrector stage involves solving a matrix equation toyield a vector of temperature increments to be added to the prediction. SLGRDJdiffers from SLGEAR in that the off-diagonal terms of the matrix in this equationare ignored. In effect, then, SLGEAR solves the temperature increment equation bymatrix inversion, and SLGRDJ by successive point iteration.$VARIABLES1 is executed at the start of each iteration within a time step and$VARIABLES2 on completion of each time step. $OUTPUTS is called at the startof the transient, every OUTINT units of time during the transient and at the end ofthe transient.

4. SLMODE

This routine performs transient analysis using the modal analysis method.Givens' method followed by the QR algorithm is used to evaluate the Eigen valuesand the Eigen vectors. The user is required to specify the following controlconstants: the time step length (DTIMEI); the problem start time (TIMEO) if this is

not 0.0; the problem time end (TIMEND) and the output interval (OUTINT). Theuser must specify a maximum iteration count (NLOOP) and relaxation criterion(RELXCA) for solution of zero capacitance nodes.If convergence to within RELXCA is not achieved inside NLOOP iterations for atime step then the solution continues but an error code is set. The control constantsDTMIN, DTMAX and DTPMAX may be set in order to regulate the time step usedby the program. DTMIN specifies the minimum time step length allowed, DTMAXthe maximum time step length allowed and DTPMAX the maximum temperaturechange allowed over a time step. Where these criteria clash, e.g. a time step smallerthan DTMIN gives a temperature change greater than DTPMAX or DTMAX setless than DTMIN, DTMIN prevails and the solution continues. If DTPMAX isexceeded because of this an error code is set.The user can specify the type of units used by setting the control constantsSTEFAN and TABS.