On Bi-grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier–Stokes Equations
✍ Scribed by S.O. Ibraheem; A.O. Demuren
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 585 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0021-9991
No coin nor oath required. For personal study only.
✦ Synopsis
In local mode analysis, the spectral radius of a particular relaxation technique computed over only the high-fre-A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of quency modes is used as a measure of the relaxation's numerical methods for solving Euler and Navier-Stokes equations. effectiveness in a multigrid scheme since, in this case, the Model problems based on the convection equation, the diffusion role of relaxation is not to reduce the total error but to equation, and Burger's equation are used to illustrate the superiority smoothen it out, i.e., to remove the high-frequency compoof the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional nents. It is assumed that the high-frequency modes have von Neumann analysis. For the Euler equations, bi-grid analysis is short wavelengths that are spatially decoupled and that all presented for three upwind difference based factorizations, namely high-frequency waves are completely ''killed'' on the fine spatial, eigenvalue, and combination splits, and two central differgrid and are not visible to the coarse grids. This, however, ence based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting is not always the case, since the intergrid processes also methods are considered. For the Navier-Stokes equations, only the influence the convergence rate. Brandt [7] presented theo-Beam-Warming (ADI) central difference scheme is considered. In retical considerations for including the transfer processes each case, estimates of multigrid convergence rates from the biin the local mode analysis in what is called the bi-grid grid analysis are compared to smoothing factors obtained from method. Also, some theoretical background is given by single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practi-Stuben and Trottenberg [4] on how to compute a more cal multigrid convergence rates for 2-D Euler and Navier-Stokes realistic amplification factor for multigrid methods based solutions based on the Beam-Warming central difference scheme, on the bi-grid analysis, and some convergence norms are and 3-D Euler solutions with various upwind difference schemes. computed for the Poisson and Helmholtz equations.
It is demonstrated that bi-grid analysis can be used as a reliable tool for the prediction of practical multigrid performance. ᮊ 1996 A number of works exist where the smoothing factor Academic Press, Inc.
has been used to predict multigrid performance in practice. However, the bi-grid analysis is becoming more attractive because of its better accuracy and reliability. Van Asselt [8]