Investigation and improvement of some recent FVM and CVFEM practices for two-dimensional, incompressible, viscous fluid flow.

摘要

Over the last decade, there has been considerable interest and success in the formulation of co-located equal-order Finite Volume Methods (FVMs) and Control-Volume Finite Element Methods (CVFEMs) for the prediction of fluid flow and heat transfer. This thesis is concerned with an evaluation and enhancement of some aspects of recent co-located equal-order FVMs and CVFEMs. In particular, the goals of this thesis are the following: (1) formulation and computer implementation of a co-located equal-order FVM that facilitates the evaluation and enhancement tasks; (2) evaluation and enhancement of iterative sequential and coupled-equation solvers; and (3) comparative evaluation of a recently proposed mass-weighted skew upwind scheme (MAW) against five well-established schemes.;The proposed equal-order co-located FVM is formulated for the prediction of steady, two-dimensional, incompressible, viscous fluid flow in planar rectangular domains. This FVM deals directly with the velocity components and pressure, or primitive variables. The rectangular domains are discretized using structured line-by-line rectilinear grids, and rectangular control volumes are constructed around each grid point. All dependent variables are co-located or stored at the same grid points, and interpolated on the same rectangular elements in an equal-order formulation. A computer program incorporating the proposed FVM has been developed and tested successfully.;On the basis of an evaluation of some available iterative solvers, two improved algorithms are proposed in this work: (1) Enhanced Sequential Solution Algorithm (ESSA); and (2) Sequential Variable Adjustment (SEVA) algorithm. Test results obtained with these algorithms are very encouraging, particularly with ESSA. The comparative evaluation of the MAW scheme shows that its performance is comparable to the skew upwind difference scheme (SUDS) of Raithby (89).