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

Abstract

Abstract:Combining iterative schemes with suitable preconditioners may improve the rate of the convergence of the methods. However, the real difficulty lies in the construction of the correct preconditioners applied to the formulated schemes. In this paper, the Modified Explicit Decoupled Group Successive Over-Relaxation method is formulated to solve the two dimensional steady-state Navier-Stokes equations. A new block splitting preconditioned matrix is applied to the formulated scheme as an effort to accelerate the convergence rate. Numerical experiments are carried out to confirm the effectiveness of the preconditioner in terms of accuracy and execution timings. Comparison with its unpreconditioned counterpart will also be reported.

A New Approach on Numerical Solutions of Burgers Equation Using PMEDG Iterative Method

“…By the same manner of the schemes presented for the Navier-Stokes problem, we v  generated are then taken to be the numerical solutions of the given problem ( [6]; [7]). …”

“… is done first using equation (2) followed by the generation of ( 1) k ij u  using equation (7).Using the equation (8) …”

A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

“…High-order schemes produce more accurate results, but suffer from slow convergence due to the increase of complexity in the algorithm. Since explicit group methods reduce algorithm complexity [28][29][30][31], we propose the use of explicit group method for the solution of two-dimensional Rayleigh-Stokes problem for a heated generalized second-grade fluid. The main purpose of this article is to solve two-dimensional Rayleigh-Stokes problem with the high-order explicit group method (HEGM).…”

Untitled

“…It is noteworthy to observe that the finite difference schemes derived from skewed (rotated) difference operators have been extensively investigated over the years for solving FPDE's. These iterative methods have been shown to be much faster than the methods based on the standard five-point formula which is due to the formers' overall lower computational complexities (Saeed and Ali [5]; Ali and Saeed [6]; Saeed and Ali [7]. In Saeed [8] the preconditioned rotated finite difference method applied successfully for solving fractional elliptic partial differential equations and the reveal results was very encouraging.…”