A direct numerical integration (DNI) method to obtain wall thermal response factors

Abstract

The solution of the problem of transient conduction in multi-layer walls through response factor method is well-known and has been studied widely and for a long time, and recent studies show that research in this field is not closed and keeps improving calculation methods of this fundamental issue in building energy performance.The aim of this work is to present an alternative to classical methods of inversion avoiding the process of root finding and approximating directly the integral Laplace's inversion formula. Previous attempts have been developed recently in this spirit, and a comparison of these methods with the one proposed will be shown in the results section.The numerical inversion considered in this work computes directly the inversion integral, using a quadrature rule, reason why this new method has been named direct numerical integration (DNI). It uses a specific integration path which makes the error diminish exponentially with the number of approximation points.The case studies will show the accuracy of the obtained results with very small computational effort and high programming simplicity.