Time step estimates for Lorentz force and thermal driven convective transport

Abstract Most physical models for fluid flow and heat transfer obey partial differential equations depending on time and space. Unsteady numerical simulations consist of a considerable number of time steps for which the stability requirement of the explicit time integration has been investigated, while, there is not a suitable method to determine the time step in the computation for fully implicit time scheme and requires a lot of trial and error process. In this paper, a direct approach to estimate the time step in unsteady computation using finite volume method is presented based on characteristic time scale of laminar convective transport phenomena. As an example, this approach is described with buoyant convection in a rectangular pool which is heated due to an electric current generated by an externally applied electric potential difference across the two vertical walls, then, Lorentz force driven convection is considered also. Our theoretical predictions are conducted through full numerical simulations. It is found that the actual time steps in numerical experiments are in good agreement with the scaling analytical predictions. The characteristic time step is deduced and predicted also, not assumed randomly, which provides a basis for the recommendation of the time step for fully implicit time scheme in the finite volume method. This is a key feature that differs from the existing numerical methods.