A divergence-free-condition compensated method for incompressible Navier-Stokes equations
Journal
Computer Methods in Applied Mechanics and Engineering
Journal Volume
196
Journal Issue
45-48
Pages
4479-4494
Date Issued
2007
Author(s)
Chiu P.H.
Abstract
The present study aims to develop a new formulation to effectively calculate the incompressible Navier-Stokes solutions in non-staggered grids. The distinguished feature of the proposed method, which avoids directly solving the divergence-free equation, is to add a rigorously derived source term to the momentum equation to ensure satisfaction of the fluid incompressibility. For the sake of numerical accuracy, dispersion-relation-preserving upwind scheme developed within the two-dimensional context was employed to approximate the convection terms. The validity of the proposed mass-preserving Navier-Stokes method is justified by solving two benchmark problems at high Reynolds and Rayleigh numbers. Based on the simulated Navier-Stokes solutions, the proposed formulation is shown to outperform the conventional segregated method in terms of the reduction of CPU time. © 2007 Elsevier B.V. All rights reserved.
Type
journal article