A higher order compact finite difference algorithm for solving the incompressible Navier-Stokes equations

A Compact Fourth - Order Finite Difference Scheme for the Steady Incompressible Navier - Stokes Equations

We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity fonn, can be approximated to fourth--order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low~to-mediwn Reynolds numbers. Numerical solutions are obtained for the model problem of ...

Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations

This article presents a family of very high-order non-uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible Navier–Stokes equations. The high-order compact schemes on non-uniform grids developed in Shukla and Zhong [R.K. Shukla, X. Zhong, Derivation of high-order compact finite difference schemes for non-uniform grid using...

Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations

This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier–Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic–parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference...

On Higher Order Finite Element Discretizations for the Incompressible Navier-stokes Equations in Three Dimensions

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...