| Summary: | 碩士 === 國立成功大學 === 航空太空工程學系 === 86 === The dissertation studies both the fixed and floating
boundarypoint grid generation of orthogonal grids. In addition
to thelinear grid equations of Ryskin and Leal, the nonlinear
gridequations, which are similar to the well known TTM
equations,are also examined.It is found that both equations
arethe Euler-Lagrange equations of properly defined
functionalwhich are functions of (x,y,f) or (ξ, η,f). The
functionsare not a strictly convex function of the
correspondingvariables (x,y,f) or (ξ, η,f). Consequently, the
reason thatthe previous study of Eca can not always find a
convergentsolution is reasonable. Several test cases show that,
if theboundary grid density is dense enough to resolve all
theboundary curvature, the floating boundary point grid
generationmethod can provide the consistency between the
distortionfunction f and boundary grids and generates smooth
orthogonal grids. Subsequently, it is found that, by employing
thefloating point method one or several times and then switching
to the fixed boundary point grid generation method,convergent
orthogonal grids can be found. Based on differentinitial grids,
this new procedure can produce differentorthogonal grid systems
which reflects the non-uniquenessof the orthogonal grid systems
for a typical domain. The othertests show that the classical
linear grid equations cangenerate a better grid orthogonality
than that of the proposed nonlinear grid equations but the grid
smoothness is worse.As comparing with the fixed boundary point
method, thefloating boundary point method can provide a better
gridsmoothness. However, if the Chikhliwala and Yortsos'
exponential function distribution of the boundary grid
pointmethod is properly employed the grid smoothness is
similarto that of the floating boundary point method.This study
also examines a exact solution of the Laplaceequation and two
free convection problems on differentorthogonal grids, all the
results show a similar tendencyprovided that the solution is
relatively smooth.
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