A Comparative Study of Explicit and Stable Time Integration Schemes for Heat Conduction in an Insulated Wall

Abstract

Calculating heat transfer in building components is an important and nontrivial task. Thus, in this work, we extensively examined 13 numerical methods to solve the linear heat conduction equation in building walls. Eight of the used methods are recently invented explicit algorithms which are unconditionally stable. First, we performed verification tests in a 2D case by comparing them to analytical solutions, using equidistant and non-equidistant grids. Then we tested them on real-life applications in the case of one-layer (brick) and two-layer (brick and insulator) walls to determine how the errors depend on the real properties of the materials, the mesh type, and the time step size. We applied space-dependent boundary conditions on the brick side and time-dependent boundary conditions on the insulation side. The results show that the best algorithm is usually the original odd-even hopscotch method for uniform cases and the leapfrog-hopscotch algorithm for non-uniform cases.

Stabil, explicit és implicit numerikus algoritmusok tesztelése vezetéses hővezetési feladatokra

“…amely az időegység alatt az anyagban létrejövő hőmennyiséget veszi figyelembe, ugyanis az anyagon belül esetlegesen lejátszódó kémiai reakciók vagy a radioaktív bomlások hőképződéssel járó folyamatok. Az előbbi (2) egyenletben szereplő  termikus diffúzivitásról feltettük, hogy az állandó, így a (2) kizárólag homogénnek tekinthető rendszerekre alkalmazható. Azon rendszerek esetében, amelyek fizikai, kémiai tulajdonságai a hely függvényében változhatnak az előbbi (2) hővezetési egyenlet helyett, annak egy általánosított alakját szükséges alkalmazni:…”

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

“…We started working on new explicit schemes a couple of years ago for determining heat conduction in any number of spatial dimensions. In our original articles [33][34][35][36][37][38][39][40], the novel algorithms were theoretically and experimentally investigated. They were proven to be stable for the linear diffusion-or diffusion-reaction equation, and their theoretical order of convergence is also stated.…”

Multi-objective optimization and simulation for multiple models of walls to estimate heat gain using Artificial Neural Network model

“…Because variables such as ambient temperature, wind velocity, and solar irradiation change over time, the design is sometimes time-dependent. In addition to ventilation and infiltration, heat gains from occupancy, equipment usage, lighting, and solar radiation through fenestration must be addressed (Kareem Jalghaf et al, 2022). As a result, numerous approaches exist to estimate a structure's energy use (Al-Sanea, 2002).…”