Numerical Solution of the Navier-Stokes Equations for Incompressible Fluid Flow by Crank-Nicolson Implicit Scheme

A High Order Numerical Scheme for Incompressible Navier-Stokes Equations

To solve the incompressible Navier-Stokes equations in a generalized coordinate system, a high order solver is presented. An exact projection method/fractional-step scheme is used in this study. Convective terms of the Navier-Stokes (N-S) equations are solved using fifthorder WENO spatial operators, and for the diffusion terms, a sixthorder compact central difference scheme is employed. The thi...

Navier-Stokes Solution by New Compact Scheme for Incompressible Flows

A new high spectral accuracy compact difference scheme is proposed here. This has been obtained by constrained optimization of error in spectral space for discretizing first derivative for problems with non-periodic boundary condition. This produces a scheme with the highest spectral accuracy among all known compact schemes, although this is formally only second-order accurate. Solution of Navi...

Numerical Solution Techniques for the Steady Incompressible Navier-Stokes Problem

In this paper we discuss some recently published preconditioners for the incompressible Navier-Stokes equations. In combination with Krylov subspace methods, they give a fast convergence for the solution of the Navier -Stokes equations. With the help of numerical experiments, we report some new findings regarding the convergence of these preconditioners. Besides that, a renumbering scheme for d...

Stabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations

This paper provides an error analysis for the Crank–Nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two-dimensional time-dependent Navier–Stokes problem, where the finite element space pair (Xh,Mh) for the approximation (uh, p n h) of the velocity u and the pressure p is constructed by the low-order finite ele...

An Upwind-Differencing Scheme for the Incompressible Navier-Stokes Equations