不可壓縮黏性熱磁流之科學計算方法
Date Issued
2005
Date
2005
Author(s)
林瑞國
DOI
zh-TW
Abstract
To preserve incompressibility constraint condition and avoid oscillations in cases of dominated convection, the major focal point of this dissertation is to develop some effective models for solving magnetic induction equations and the incompressible Navier-Stokes equations. In the simulation, there is one major source of instability due to an inappropriate storage of the velocity and pressure fields. This type of instabilities usually appears as oscillations seen primarily in the pressure filed. The other instability source is due to the presence of advection terms in the equations, which can result in spurious oscillations in the velocity field. These two challenging instability problems form are core of the present study.
To solve the CD (convection-diffusion) model equation the FDM (finite-difference method) for the field equations under current investigation is developed on non-staggered grids. The unconditional mass conservation, the approximation of discrete convection terms, the acceleration of convergence are considered in the proposed method. The FDM is employed along with the compact scheme and the DRP (dispersion-relation-preserving) theory to overcome the convective instability that arises from the convection term for problems considered at high Reynolds numbers has been employed to enhance stability. A novel method in non-staggered grids to accelerate the nonlinear convergence of incompressible Navier-Stokes equation is also proposed. To validate these proposed methods, several 2D and 3D test cases were performed. The simulated results show that the proposed methods are highly reliable and applicable to a wide range of flow conditions. For unsteady problems, a high order multiple time-stepping scheme, which increase the time accuracy, is introduced. Linearization and multi-level methods were proposed for effectively accelerating the non-convergence arising from the convection term.
Subjects
有限差分
不可壓縮流
磁場方程
精確解
緊致格式
保有頻散格式
finite-difference
incompressible viscous flow
magnetic induction equation
nodally-exact scheme
compact scheme
DRP scheme
Type
thesis
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