Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges

Abstract

Several previous experiments showed that the leapfrog–hopscotch and the adapted Dufort–Frankel methods are the most efficient among the explicit and stable numerical methods to solve heat transfer problems in building walls. In this paper, we extensively measure the running times of the most successful methods and compare them to the performance of other available solvers, for example, ANSYS transient thermal analysis and the built-in routines of MATLAB, where three different mesh resolutions are used. We show that the running time of our methods changes linearly with mesh size, unlike in the case of other methods. After that, we make a long-term simulation (one full winter month) of two-dimensional space systems to test the two best versions of the methods. The real-life engineering problem we solve is the examination of thermal bridges with different shapes in buildings to increase energy efficiency.