The Calculation (Solver)
Besides the knowledge of geometrical and physical composition of a building construction the calculation the temperature distribution within a building construction requires the knowledge of particular boundary conditions also. The approach used in this program is founded on top of specific boundary conditions - those defining the air temperature of each space connected to the construction. At cut-off planes an implicit adiabatic boundary condition is applied automatically by forcing the normal component of heat flux to zero, thus no additional user input is required. Therefore the user needs to provide particular air temperatures only. It is to be considered that only uniform air temperature shall be assigned to particular space, thus effects like variation of temperature due to air flow layers cannot be input directly. If heat sources are present within the construction additional boundary conditions defining the heat density of each particular source have to be supplied also.
A characteristic of the program is the division of the procedure for generating a temperature distribution into two stages: calculation of base solutions and evaluation under prescribed conditions.
Heat flow in a building construction, as well as the subsequent temperature distribution, can be described mathematically by differential equations. Most importantly, these equations are linear and homogenous by nature. This means that one set of solutions, calculated for a specific set of conditions, can be "re-used" as the basis for solutions under differing conditions by superposition, i.e. by linear combination of selected base solutions (see "Theoretical background"). More specifically, base solutions are calculated under the assumption of a "basic" set of boundary conditions: with an air temperature of 1 in the selected space, and 0 in all others.
The calculation approach in the program uses this circumstance to minimise over-all evaluation time for user's comfort. One set of base solutions need be calculated only once to characterise a given model, which can subsequently be considered under varying conditions without repeating the time-consuming computation necessary to solve the primary set of differential equations. The superposition under applied boundary conditions is postponed to the evaluation part, thus the determination of basic solutions in that step does not require any input of particular boundary conditions.
Computation time is further reduced by utilising the weighting function character of base solutions (normalised such that their sum must equal 1). Hence, if N cases have been selected, only N−1 solutions need to actually be calculated. The N-th base solution is then very simply derived as a difference of the sum to 1, that is, by a separate stage of superposition.
If heat sources are present within the construction too, respective base solution will be created for each particular heat source also. The calculation is provisioned by setting the heat density of particular source to 1 while leaving all other boundary conditions at 0. Therefore the total number of base solutions calculated is the sum of the number of spaces and the number of heat sources.
The parameters of iteration can be manipulated by the user prior to a calculation run of course. This is of interest when a model is particularly complex or when base solutions which have already been calculated prove to be inadequately precise during subsequent evaluation.