*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*: *g*_{j}(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. |