Table of Contents
Solver control parameters for a transient problem
The XT2T/XT3T solver control parameters are specified in the name.iB file:
IP KREST 0 KOUT INT3 NSAX NSTEPX 0 RP TIMS ERAL EDIF TOL DTRUN PIVOT PENAL
KREST is the restart key:
$=1$ … new computation
$=3$ … continuation of a successfully completed computation
KOUT is the log output key:
$=1$ … sequence of all approximations
$=2$ … solution only
INT3 is the (time) integration step index from which to resume when $\mathtt{KREST}=3$. When $\mathtt{KREST}=1$, $\mathtt{INT3}=0$.
NSAX is the maximum number of successive approximations before initiating a new matrix factorization. The recommended value is $10<\mathtt{NSAX}<20$.
NSTEPX is the maximum allowed number of time steps for the entire calculation (when using automatic time step selection).
TIMS is the solution start time $[\text{s}]$. When $\mathtt{KREST}=3$, $\mathtt{TIMS}=0$.
ERAL is the convergence criterion for the residual. The recommended value is $10^{-5}<\mathtt{ERAL}<10^{-2}$. It applies only when $\mathtt{KAPPR}=1$.
EDIF is the convergence criterion for the temperature increment $[^\circ\text{C}]$. The recommended value is $1<\mathtt{EDIF}<10$. It applies only when $\mathtt{KAPPR}=1$.
TOL is the error tolerance within a single time step $[^\circ\text{C}]$, used only for automatic time step selection when $\mathtt{KAUTO}=1$. The recommended value is $1<\mathtt{TOL}<10$.
DTRUN is the elementary time step $[\text{s}]$. The actual time step length is rounded to an integer multiple of $\mathtt{DTRUN}$. It is considered only for $\mathtt{DTRUN}>10^{-6}$.
PIVOT is the minimum allowed pivot value during matrix factorization. The default value is $10^{-6}$.
PENAL is the penalty function value for connector elements of all types. The default value is $10^6$.
Note
The $\mathtt{TIMS}$ parameter is only a formal quantity. The shift of the time axis serves to simplify the description of time dependencies.
For each load case—representing a time interval of the solution—the following must be specified within the AS batch:
AS load case number /$\dots$ /R TIMX STEP TSC /$\dots$
TIMX is the end of the time interval $[\text{s}]$.
STEP is the integration step size $[\text{s}]$. In the case of automatic time step control ($\mathtt{KAUTO}=1$), $\mathtt{STEP}$ is the initial size of the first step.
TSC is the integration method constant, $0\le\mathtt{TSC}\le1$. $\mathtt{TSC}=0$ corresponds to the explicit method, while $\mathtt{TSC}=1$ (recommended) represents a fully implicit scheme.
It is also recommended to activate the AV set:
AV set number T 6 N KAPPR KAUTO KPRED V 4*0
by assigning it in the AS batch:
AS load case number /$\dots$ /A set number /$\dots$
KAPPR is the successive approximation key:
$=0$ … without using an iterative method
$=1$ … with iterations controlled by criteria $\mathtt{ERAL}$ and $\mathtt{EDIF}$ (recommended)
KAUTO is the automatic time step control key:
$=0$ … user-controlled
$=1$ … automatic control (recommended)
KPRED is the thermophysical properties prediction key:
$=0$ … without prediction
$=1$ … with prediction (recommended when $\mathtt{KAUTO}=1$)
In the first load case (AS 1), it is necessary to specify the initial temperature field using a GV set.
Each load case corresponds to as many records in the name.STR and name.TEM files as the number of integration steps performed.
Integration scheme
For the integration of differential equations in time, a generalized one-step method with the $\mathtt{TSC}$ parameter is used. The value $\mathtt{TSC}=0$ corresponds to the explicit forward Euler method, which linearizes the equations, with the solution corresponding to a sequence of piecewise linear changes (processes). Although this method does not require any iterations, instabilities may occur, i.e., temperature oscillations at nodal points. A careful inspection of the results is then required, so the use of this method is not recommended.
Values of $\mathtt{TSC}>0$ always lead to an implicit method with the unconditional stability condition $\mathtt{TSC}\ge0.5$. The case $\mathtt{TSC}=1$ represents the fully implicit backward Euler method. Implicit integration requires iterations because a nonlinear system of equations must be solved at each time step. The Commentary regarding the parameters $\mathtt{ERAL}$, $\mathtt{EDIF}$, $\mathtt{TOL}$, and $\mathtt{KAPPR}$ remains valid without change.
The value of $\mathtt{NSAX}$ determines the maximum number of iterations in each time step. It is recommended to assign the AV set with $\mathtt{KAPPR}=1$ in each load case. For reasons of stability, it is advisable to iterate until convergence in each time step, i.e., to choose a somewhat higher value of $\mathtt{NSAX}$ so that the number of iterations in each step is determined by $\mathtt{EDIF}$ and $\mathtt{ERAL}$ rather than by reaching $\mathtt{NSAX}$.
Time step
The solution follows a sequence of load cases in time. Each load case must be assigned a value of $\mathtt{TIMX}$, which is the time until which the current assignment applies. As soon as $t=\mathtt{TIMX}$ is reached, the existing assignment is replaced by a new load case.
The $\mathtt{STEP}$ value is the integration step size prescribed by the user. This size can vary in each load case (interval). However, it should be kept in mind that changing the integration step size requires matrix refactorization. If the integration is controlled automatically, $\mathtt{STEP}$ is the initial step size.
Automatic control is initialized in each load case (interval) by $\mathtt{KAUTO}=1$ specified via the AV set (its use is not recommended for $\mathtt{TSC}=0.5$ or $\mathtt{TSC}=0$). With automatic control, the integration step size is increased if $$\mathtt{PLTE}<0.25\,\mathtt{TOL},$$ where $\mathtt{PLTE}$ is the estimated local truncation error [$^\circ\text{C}$]. The integration step size is decreased for $$\mathtt{TOL}<\mathtt{PLTE}.$$ The $\mathtt{TOL}$ value is specified on the RP line. The calculated integration step size is rounded to an integer multiple of $\mathtt{DTRUN}$. This time thus represents an elementary quantum (with respect to outputs).
In load cases where $\mathtt{KAUTO}=1$, the total number of time steps from the beginning of the calculation is tracked. If it exceeds the $\mathtt{NSTEPX}$ value, the calculation is terminated.
Restart of computation
If the computation has completed successfully, it is possible to continue the solution by specifying additional load cases with $\mathtt{KREST}=3$. On the IP line, it is then necessary to specify the integration step index $\mathtt{INT3}$ from which to start (inclusive). If the computation is to be restarted from the end of the last solution, it is specified as $$\mathtt{INT3}=1+\sum\mathtt{NSTEP}_i,$$ where $\mathtt{NSTEP}_i$ is the number of integration steps in the $i$-th load case (interval) and the summation is performed over all load cases.
Prediction of thermophysical properties
Before starting the calculation in a time interval, it is possible to estimate the values of quantities by extrapolation from the previous step, which can speed up the calculation and improve convergence. Prediction is enabled by $\mathtt{KPRED}=1$, which is specified via the AV set and applies within the corresponding load case.
