A comparative study on the performance of two time stepping schemes for convection in a fluid-saturated porous medium (Q2729155)

The author carries out a comparative study to evaluate the performance of two different time stepping schemes based on velocity correction procedure for natural covection in a fluid-saturated porous medium. The first scheme is semi-implicit (SI) one, in which the linear and nonlinear porous medium terms of the momentum equation are treated implicitly, but the solution of simultaneous systems is avoided by lumping the mass. The second procedure (quasi-implicit, QI) treats the porous medium and viscous terms implicitly, and a simultaneous equation system is constructed to solve the equations of momentum conservation.NEWLINENEWLINENEWLINEBoth the schemes are tested on two different problems. Although the QI scheme gives faster convergence to steady state in both Darcy and non-Darcy regimes at lower Rayleigh numbers and on fine meshes, the SI scheme has the advantage of speed at higher Rayleigh numbers, especially in the Darcy flow regime. On the coarse mesh used, the SI scheme has the clear advantage of efficiency over the QI scheme.NEWLINENEWLINENEWLINEAnother point of practical interest is that QI schemes can be used to calculate transients accurately without any futher modifications to the code, but SI schemes need modifications. However, features such as the simplicity of the SI scheme and its CPU advantages over QI scheme in some flow region even on a fine mesh are worth noting.