Analysis of Numerical Error in One-Dimensional Storage Tank Models for Solar Energy System Simulations

This study investigates the temperature profiles predicted by trnsys one-dimensional (1D) thermal storage tank models for typical charging conditions. Simulation parameters, such as grid spacing and time-step size, were varied to observe the changes in the numerical error when compared with an exact analytical solution. A Taylor series expansion was also performed on the discretized, 1D, advection–diffusion equation to obtain an expression for this numerical error. A numerical diffusion term was found which could be used to improve the prediction of the temperature profile in a storage tank simulation. Finally, the influence of this error on predictions of the annual solar fraction for a domestic hot water system was explored.