On error estimates of the projection method for the time-dependent natural convection problem: First order scheme. (September 2016)

• Record Type: Journal Article
• Authors: Qian, Yanxia; Zhang, Tong
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 5(2016)
• Page Start: 1444
• Page End: 1465
• Publication Date: 2016-09
• Subjects: Natural convection problem -- Projection method -- Stability -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.07.013
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this article, a projection method (or fractional step method) is proposed and analyzed for the time-dependent natural convection problem in two dimensions. Based on this method, the considered problem is decoupled into two subproblems: one is for the velocity and temperature, and the other is for the pressure. Firstly, a linear elliptic equation is treated for the temperature; Then, a linear elliptic equation is solved for the velocity; Finally, a Poisson equation is considered for the pressure. Stability is performed and the convergence results of the projection method are derived. Furthermore, a modified projection scheme which leads to some improved error estimates is also proposed. Finally, some numerical examples are presented to verify the established theoretical findings.