A Family of Second Order Time Stepping Methods for the Darcy-Brinkman Equations
For researchers simulating double-diffusive convection in porous media, this provides a more accurate and stable numerical method, though it is an incremental improvement over existing approaches.
This paper develops an unconditionally stable second-order time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection, proving convergence and demonstrating accuracy through numerical examples.
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing the curvature for velocity, temperature and concentration equations. Accuracy in time is proven and the convergence results for the fully discrete solutions of problem variables are given. Several numerical examples including a convergence study are provided that support the derived theoretical results and demonstrate the efficiency and the accuracy of the method.