A Family of Second Order Time Stepping Methods for the Darcy-Brinkman Equations

TL;DR

This paper introduces a new second-order, unconditionally stable time stepping scheme for the Darcy-Brinkman equations, enhancing accuracy and efficiency in modeling double-diffusive convection.

Contribution

The paper develops a novel second-order time stepping method with stabilization for Darcy-Brinkman equations, ensuring unconditional stability and proven accuracy.

Findings

Method is unconditionally stable and accurate.

Numerical examples confirm theoretical convergence.

Demonstrates efficiency in double-diffusive convection simulations.

Abstract

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.