TIME STEP ESTIMATES FOR LORENTZ FORCE DRIVEN CONVECTIVE TRANSPORT
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 implicit time integration and it costs plenty of test trial and error process. In this paper, a straightforward approach to estimate the time step in transient computations 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 electric current generated by an externally applied electric potential difference across the two vertical walls. Our theoretical predictions are verified by full numerical simulations. It is found that the numerical results are in good agreement with the scaling analytical predictions. The time step is deduced and predicted, not assumed randomly, that is a key feature differed from the existing numerical methods unrelated to the inherent physical parameter.