A comparative study on the performance of two time stepping schemes for convection in a fluid saturated porous medium

A comparative study has been carried out to investigate the performance of two different time stepping schemes for convective heat transfer and flow in a fluid saturated porous medium. Both the schemes are based on the velocity correction procedure. The first scheme is a semi‐implicit one in which the linear and non‐linear porous medium terms of the momentum equation are treated implicitly but solution of the simultaneous equation system is avoided by lumping the mass. The second procedure (quasi‐implicit) treats the porous medium and viscous terms implicitly and a simultaneous equation system is constructed to solve the equations of momentum conservation. Two numerical examples have been considered and both the schemes are tested for various parameters governing the flow and heat transfer in these problems. Results show that, at smaller Rayleigh numbers and on fine meshes, the quasi‐implicit scheme gives faster convergence to steady state in both Darcy and non‐Darcy regimes than that of the semi‐implicit scheme. At higher Rayleigh numbers, the semi‐implicit scheme is faster in the Darcy regime. Also, the semi‐implicit scheme is faster than that of the quasi‐implicit scheme on a coarse mesh used in this study. In general both the schemes predict transient cyclic developments well.