Hi,
i have problems to understand the given information in the convergence analyzer.
The performed calculation was made for a very simple flat roof with materials from the WUFI database, a 50:150 grid, recommended timesteps and common indoor and outdoor conditions. The analyzer gives the following info:
1500 iterations performed
last residual:
theta: 8.309E-003
phi: 8.877E-002
What does it say? If its bad news, how do i know what to change or improve?
Many thanks for your help!
Regards,
Martin
convergence analyzer 2
Re: convergence analyzer 2
Solution Process
The solution process is split into 4 loops
Time Loop
The time loop performs the number of desired time steps.
Rain Loop
Adaptation of the coefficients for liquid transport at the surface. This has to be a separate loop for stability reasons. It is controlled by the rain residual and a hard-coded upper bound for the number of cycles.
Inner Loop
Because of the non-linear characteristics of the equations the coupling of heat and moisture is achieved by holding the temperature fixed and solving the state only for the humidity and then vice versa. This is repeated until either the residuals are less than a user-supplied convergence criterion or a maximum number of cycles is reached.
Solver Loop
To speed up the solution of the linear equation system (sparse matrix) an iterative solver is used. The accurace and therewith the time used for the solution process of the linear equation system can be changed by the user.
Solution Process - Residuals
Rain Residual and control of rain loop
The maximum absolute change of the liquid transport coefficients involved is recorded. This number is checked against the overall convergence criterion to determine if another cycle is required. This loop terminates after a maximum of
10 cycles in the current version.
Inner Residual and control of inner loop
The inner residuals are the maximum absolute change of the temperature and humidity field. As long as these residuals are greater than the convergence criterion the coefficients of the equations for the temperature and humidity fields are updated and the linear equation systems are solved again. This loop stops after a user-defined maximum of cycles in case the residuals do not reach the convergence criterion or if there is no significant change in both temperature and humidity residual during a few cycles.
SIP (strongly implicit procedure) Solver by Stone [FP02] [Sto68]
Lower-upper decomposition method specially designed for the solution of partial differential equations. A correction of the initial field is calculated by solving two triangular systems. The quality of the solution is checked by a residual which is the relative change of the obtained solution. The smaller the change the more accurate the solution. Because we solve for both the temperature and the humidity field in the inner loop more than once there is no need for an exact solution per cycle. But be aware: if you intend only to solve the temperature or humidity equation you have to adjust the controlling parameters.
An alternative to this solver is the ADI (alternate direction iteration) Solver [NR89]
Here either the x- or y-directional parameters are held constant (by adding the relevant quantities to the result vector) and the resulting triangular systems are solved. This is repeated for a maximum of 80 sweeps or a maximum absolute change smaller than a hard-coded number of 5E-6. The same argumentation as in SIP applies to ADI – the solutions do not have to be that exact because of the iterative process of the global solution strategy.
Control Parameter
Outer Loop Control
To speedup the solution process to get an first overview you can use a small maxit.
Radial Diameter
Measured from the left edge – larger than zero for cylindrical coordinates
Print residual at iteration modulo
e.g. “10” means print residual each tenth iteration
Solver Settings
Inner Loop Control
[FP02] FERZIGER JOEL H., PERIC MILOVAN:
Computational Methods for Fluid Dynamics. Springer, 2002
[Sto68] STONE, HERBERT L.:
Iterative Solution of implicit approximations of multidimensional partial
differential equations. SIAM J. Numer. Anal., Sept. 1968
[NR96] PRESS , WILLIAM H., BRIAN P. FLANNERY, SAUL A. TEUKOLSKY and WILLIAM T. VETTERLING:
Numerical Recipes in Pascal. Cambridge University Press, 1996.
The solution process is split into 4 loops
Time Loop
The time loop performs the number of desired time steps.
Rain Loop
Adaptation of the coefficients for liquid transport at the surface. This has to be a separate loop for stability reasons. It is controlled by the rain residual and a hard-coded upper bound for the number of cycles.
Inner Loop
Because of the non-linear characteristics of the equations the coupling of heat and moisture is achieved by holding the temperature fixed and solving the state only for the humidity and then vice versa. This is repeated until either the residuals are less than a user-supplied convergence criterion or a maximum number of cycles is reached.
Solver Loop
To speed up the solution of the linear equation system (sparse matrix) an iterative solver is used. The accurace and therewith the time used for the solution process of the linear equation system can be changed by the user.
Solution Process - Residuals
Rain Residual and control of rain loop
The maximum absolute change of the liquid transport coefficients involved is recorded. This number is checked against the overall convergence criterion to determine if another cycle is required. This loop terminates after a maximum of
10 cycles in the current version.
Inner Residual and control of inner loop
The inner residuals are the maximum absolute change of the temperature and humidity field. As long as these residuals are greater than the convergence criterion the coefficients of the equations for the temperature and humidity fields are updated and the linear equation systems are solved again. This loop stops after a user-defined maximum of cycles in case the residuals do not reach the convergence criterion or if there is no significant change in both temperature and humidity residual during a few cycles.
SIP (strongly implicit procedure) Solver by Stone [FP02] [Sto68]
Lower-upper decomposition method specially designed for the solution of partial differential equations. A correction of the initial field is calculated by solving two triangular systems. The quality of the solution is checked by a residual which is the relative change of the obtained solution. The smaller the change the more accurate the solution. Because we solve for both the temperature and the humidity field in the inner loop more than once there is no need for an exact solution per cycle. But be aware: if you intend only to solve the temperature or humidity equation you have to adjust the controlling parameters.
An alternative to this solver is the ADI (alternate direction iteration) Solver [NR89]
Here either the x- or y-directional parameters are held constant (by adding the relevant quantities to the result vector) and the resulting triangular systems are solved. This is repeated for a maximum of 80 sweeps or a maximum absolute change smaller than a hard-coded number of 5E-6. The same argumentation as in SIP applies to ADI – the solutions do not have to be that exact because of the iterative process of the global solution strategy.
Control Parameter
Outer Loop Control
- Time Step in seconds
Number of Time Steps
- Maxit: maximum number of iterations to perform
Convergence Criterion: continue with next time step if satisfied
To speedup the solution process to get an first overview you can use a small maxit.
Radial Diameter
Measured from the left edge – larger than zero for cylindrical coordinates
Print residual at iteration modulo
e.g. “10” means print residual each tenth iteration
Solver Settings
Inner Loop Control
- URF: Underrelaxation factor. Blend the current solution with the previous solution in each cycle of the inner loop. If you encounter a big change in humidity (that usually results in high diffusive fluxes) together with bad convergence you should reduce this number. Usually you will only achieve an effect by reducing the URF for the humidity equation. In the temperature equation only the heat source from evaporational and/or melting processes is underrelaxed. But only if the linearization of this source term would lead to an unstable system. To check if the heat source is causing convergence problems you can exclude the effects of evaporation and/or melting.
NOR: Residual normalization factor. The amplitude of temperature changes is approximately 50 times the amplitude of relative humidity changes. This factor is used to scale the two residuals to reach about the same order of magnitude for making them more comparable.
- SOR: Convergence criteria. Relative change of correction in SIP
NSW: Number of iterations allowed to reach SOR
- ADI: Alternate direction iteration. Use ADI instead of the recommended
SIP Solver.
[FP02] FERZIGER JOEL H., PERIC MILOVAN:
Computational Methods for Fluid Dynamics. Springer, 2002
[Sto68] STONE, HERBERT L.:
Iterative Solution of implicit approximations of multidimensional partial
differential equations. SIAM J. Numer. Anal., Sept. 1968
[NR96] PRESS , WILLIAM H., BRIAN P. FLANNERY, SAUL A. TEUKOLSKY and WILLIAM T. VETTERLING:
Numerical Recipes in Pascal. Cambridge University Press, 1996.