The alternating group explicit (AGE) iterative method for solving a Ladyzhenskaya model for stationary incompressible viscous flow

Preconditioned Modified Explicit Decoupled Group for the Solution of Steady State Navier-Stokes Equation

“…This table shows the discrete L 2 norm ψ * − ψ L 2 where ψ denotes the computational solution on an n×n grid (h=1/n) and ψ * is the exact solution. It is observed that the results behave in similar manner as in [6].…”

“…We can also observe that the proposed preconditioned MEDG SOR scheme has shown considerable improvement in the number of iterations and execution time compared to that of the preconditioned scheme displayed in Ali and Saeed [13]. It is observed that our model problem is same as the problem in [6] when Re = 0 and ∈ 1 = 0 in Eq. (2).…”

“…Suppose we impose the boundary conditions ψ = 0 and ∂ 2 ψ ∂ η 2 = 0, where η is the normal to the boundary ∂ Ω of Ω , then our problem amounts to solving (1) and (2) successively with ψ = 0 and ω = 0 respectively along ∂ Ω . Over the last few decades, there have been some interests in designing new methods for solving these stream-vorticity formulations ( [2], [3], [4], [5], [6]). In particular, Ali and Abdullah [4] derived a group explicit method derived from a skewed five-point finite difference approximations where the proposed method was shown to be more efficient in CPU timings than the existing schemes based on the standard five-point difference stencil.…”

A block preconditioning technique for the streamfunction‐vorticity formulation of the Navier‐Stokes equations

“…The focus of this study is the efficient solution to the linear system (12). This linear system (12) is nonsymmetric and indefinite.…”

“…Iterative solutions of systems of the form (12) can be found using a variety of methods. In particular, Krylov subspace methods (see for example [6]) such as GMRES are applicable for such nonsymmetric systems (12). It is known that the performance of Krylov subspace methods is usually sensitive to the conditioning of the coefficient matrix and thus the idea of preconditioning must be implemented.…”