A numerical method for solution of incompressible Navier–Stokes equations in streamfunction‐vorticity formulation. Issue 6 (6th September 2021)

• Record Type: Journal Article
• Authors: Raza, Saad; Rauf, Abdul; Sabi'u, Jamilu; Shah, Abdullah
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 6(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-09-06
• Subjects: conforming finite element method -- diagonally implicit fractional‐step θ−scheme -- DUNE‐PDELab -- streamfunction‐vorticity formulation -- the incompressible Navier–Stokes equations; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1188
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: In this work, we have proposed a numerical approach for solving the incompressible Navier–Stokes equations in the streamfunction‐vorticity formulation. The numerical scheme is based on the diagonally implicit fractional‐step θ − (DIFST) method used for the time discretization and the conforming finite element method for the spatial discretization. The accuracy and efficiency of the scheme are validated by solving some benchmark problems. The numerical simulations are carried out using the DUNE‐PDELab open‐source software package. The comparison of DIFST scheme with different time discretization schemes is provided in terms of CPU time. Also, different solvers with preconditioners are investigated for solving the resulting algebraic system of equations numerically.