On space–time ratio in the soybean mass aeration problem using a manufactured solution with realistic parameters

Abstract

The purpose of this paper is to introduce a new manufactured analytical solution to the mathematical model that describes the behavior of the grain mass aeration process, proposed by Thorpe, using the method of manufactured solutions. The finite difference method, utilizing the CDS-Crank-Nicolson and Leith’s methods, was employed. An error analysis of the approximations used was performed to verify the effective and apparent orders of the discretization error obtained with mesh refinement. Furthermore, a study on the space–time ratio in the numerical methods was carried out in two realistic settings of soybeans aeration process. It was observed that Leith's method outperformed the CDS-Crank-Nicolson method. Therefore, Leith's method is recommended by this paper to numerically solve the grain mass aeration model proposed by Thorpe, given its robustness with respect to the space–time ratio in both settings studied.