Basics and Some Theory of AnTherm
Method of Analysis
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.
| base solutions | 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. 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.
Thus the temperature distribution, a function of the three spatial coordinates, can ultimately be written in the simple form of a sum of temperature values. The individual temperatures are the result of the actual boundary conditions (air temperatures in the given spaces from 0 to m) weighted by dimensionless base solutions:
In other words, base solutions are effectively a generalised form of weighting factors (g-values) - a function of position for a given space, j: gj(x,y,z). The calculation approach in the program AnTherm uses this circumstance to minimise over-all evaluation time. One set of base solutions need be calculated only once to characterise a given model, which can subsequently be considered under varying boundary conditions without repeating the time-consuming computation necessary to solve the primary set of differential equations. 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. |
