Computational Aero-Acoustic Using High-order Finite-Difference Schemes

Computational Aero-Acoustic Using High-order Finite-Difference Schemes

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 ...

High-order finite difference schemes for incompressible flows

This paper presents a new high order approach to the numerical solution of the incompressible Stokes and Navier-Stokes equations. The class of schemes developed is based upon a velocity-pressure-pressure gradient formulation which allows: (i) high order finite difference stencils to be applied on nonstaggered grids; (ii) high order pressure gradient approximations to be made using standard Padé...

An Overview of Some High Order and Multi-Level Finite Difference Schemes in Computational Aeroacoustics

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by . 0 = ∂ ∂ + ∂ ∂ x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised s...

An overview of high-order finite difference schemes for computational aeroacoustics

One of the problems in computational aeroacoustics (CAA) is the large disparity between the length and time scales of the flow field, which may be the source of aerodynamically generated noise, and the ones of the resulting acoustic field. This is the main reason why numerical schemes, used to calculate the timeand space-derivatives, should exhibit a low dispersion and dissipation error. This p...