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Adaptive Unified Coordinate Method And The Application Of Two-dimensional Complex Flow Field

Posted on:2007-07-26Degree:MasterType:Thesis
Country:ChinaCandidate:W YaoFull Text:PDF
GTID:2190360212960746Subject:Fluid Mechanics
Abstract/Summary:PDF Full Text Request
Recently, the unified coordinate system is introduced by W.H.Hui and his co-workers which introduced an arbitrary parameter h. In this system, the flow variables are considered to be functions of time and of some pseudo-particles which move with velocity hq, q being the velocity of fluid particles. It includes the Eulerian coordinates as a special case when h=0, and the Lagrangian when h=1. Freedom in choosing h makes it possible to take the advantages of the Eulerian and the Lagrangian and to avoid their disadvantages. It can avoid excessive numerical diffusion and difficulty in capturing moving boundaries in Euler coordinates, it also can avoid severe gird deformation in the Lagrange coordinates, yet it remains sharp resolution of slip lines. In this paper, the solution of Riemann problem for 1-D Euler equations obtained from 2-D Euler equations after dimensional splitting is given, a few numerical simulation results of 1-D and 2-D dynamics problems, which use the unified coordinate system and the Godunov scheme with MUSCL update, show simplicity and practicability of the scheme. Moreover, variational methods are used in the unified coordinate system, the mesh spacing, smoothness, orthogonality and regularity of grids generated are also considered to get the distribution of h. Some typical examples demonstrate that variational methods used in the unified coordinate system is possible, and the distribution of h can be adjusted by given different boundary conditions, so as to get adaptive meshes for idiographic physical problems.
Keywords/Search Tags:the unified coordinate system, Euler equations, Riemann problem, MUSCL scheme, Godunov scheme, moving mesh, variational methods, elliptic equation
PDF Full Text Request
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