A Non-Conforming Least Squares Spectral Element Formulation for Oseen Equations with Applications to Navier-Stokes Equations. (2nd October 2016)

• Record Type: Journal Article
• Authors: Mohapatra, Subhashree; Ganesan, Sashikumaar
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 10(2016)
• Page Start: 1295
• Page End: 1311
• Publication Date: 2016-10-02
• Subjects: Least-squares methods -- Navier-Stokes equations -- Oseen equations -- spectral element methods; 76D07 -- 65M70 -- 65M12; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1209518
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we propose a non-conforming exponentially accurate least-squares spectral element method for Oseen equations in primitive variable formulation that is applicable to both two- and three-dimensional domains. First-order reformulation is avoided, and the condition number is controlled by a suitable preconditioner for velocity components and pressure variable. A preconditioned conjugate gradient method is used to obtain the solution. Navier-Stokes equations in primitive variable formulation have been solved by solving a sequence of Oseen type iterations. For numerical test cases, similar order convergence has been achieved for all Reynolds number cases at the cost of higher iteration number for higher Reynolds number.