# validation of solution methods for building energy simulation

A dynamic thermal model of a building and its associated heating/cooling plant is a set of differential equations describing the interactions of the system components. The equations originate in building physics, plant thermodynamics and control theory. The major mathematical techniques used to solve these equations are (time and frequency) response function methods and finite difference methods.

The accepted validation methodology for building energy simulation software, which has recently been standardised in ANSI/ASHRAE Standard 140, has as its main elements:

(a) Empirical validation - in which program predictions are compared to measured data from a real structure.

(b) Analytical verification - in which output from a program is compared with an exact solution for a simple, tractable problem.

(c) Inter-model comparison - in which program predictions are compared with those of other, better trusted programs.

Method (a) gives an estimate of total (including measurement and modelling) error and not just mathematical (including truncation and stability) error. Method (c) does not involve an absolute standard. Only (b) tests the solution method exclusively. But the boundary conditions used are usually very simple and the test examples themselves are too confined to be representative of the building energy problem. Nevertheless, rigorous and comprehensive testing of solution methods is imperative in that deficiencies in the solver have a global impact on performance whereas errors in any of the constituent models probably have a more limited effect.

The validation method employed in the present study, described as a numerical experiment, makes use of a highly accurate solution generated by applying a convergent numerical method with a sufficiently small time step to a test problem of realistic scale and complexity. Two such solutions were produced, using different numerical methods, and their average formed the reference solution. The two solutions differed from each other by less than one-ten-thousandth of a degree typically. All useful numerical methods, including those used to produce reference solutions in this study, have been shown to be convergent and consequently the reference solution approaches the exact solution as the time step is reduced. Test solutions generated using various mathematical techniques can then be compared with the reference solution and inferences drawn. Clearly, the only significant error present in a numerical experiment is that associated with the solver under test. Many variants of a very detailed dynamic thermal model of a room, which includes a proportionally controlled terminal unit, are used as test problems in this work. A collection of recently developed implicit numerical methods, together with some more traditional ones, are ranked using this validation method. The metric to be used is computational efficiency which is here defined to be the inverse of the product of numerical error and execution time.

## Personnel

DIT - School of Civil & Building Services Engineering

Dr Michael Crowley