Control strategies for timestep selection in simulation of coupled viscous flow and heat transfer

This work investigates the use of control strategies for timestep selection and convergence rate improvement of non‐linear iterative processes in the finite element solution of 2D coupled viscous flow and heat transfer. The present solution method employs a decoupled scheme, where the finite element flow formulation is based on a penalty Galerkin method and the heat transfer computations use a traditional Galerkin formulation. We compare the efficiency of the control strategies for timestep selection with another heuristic adaptive stepsize selection scheme. Numerical results for representative Rayleigh–Benard–Marangoni problems confirm that the non‐dimensional kinetic energy could be a suitable parameter to improve the timestep selection when co‐ordinated with the convergence control of non‐linear iterations. We find approximate solutions with a much smaller number of steps without any significant loss of accuracy.