A Decoupled, Parallel, Iterative Finite Element Method for Solving the Steady Boussinesq Equations

Abstract

In this work, a decoupled, parallel, iterative finite element method for solving the steady Boussinesq equations is proposed and analyzed. Starting from an initial guess, an iterative algorithm is designed to decouple the Naiver-Stokes equations and the heat equation based on certain explicit treatment with the solution from the previous iteration step. At each step of the iteration, the two equations can be solved in parallel by using finite element discretization. The existence and uniqueness of the solution to each step of the algorithm is proved. The stability analysis and error estimation are also carried out. Numerical tests are presented to verify the analysis results and illustrate the applicability of the proposed method.