Development of an upwind point collocation meshfree method for hyperbolic equations = 쌍곡형 방정식을 위한 upwind point collocation meshfree method의 개발

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Recently much attention has been drawn to meshfree method since conventional methods such as Finite Difference Method (FDM), Finite Volume Method (FVM) and Finite Element Method (FEM) have suffered from difficulty of mesh generation for complex geometry. In particular, Point Collocation Meshfree Method (PCMM) is attractive among the meshfree methods because it can be regarded as a truly meshfree method. Up to now, however, PCMM for hyperbolic equations has not been possible in the literature due to the lack of innate dissipation mechanism necessary to suppress numerical oscillation by the convective terms. In the present paper, an upwind PCMM is developed using Local Point Approach (LPA). The key idea of LPA is that conservative variables are obtained by meshfree approximation at the auxiliary local points which are not necessarily nodes, on which any upwind scheme of FDM or FVM can be applied to calculate the convective terms. For space approximation, Fast Moving Least Square Reproducing Kernel Method (FMLSRK) is employed. For validation purpose, linear advection equation and inviscid Burgers equation are solved by the present scheme. Various test problems of Euler equations are also calculated to demonstrate application of the scheme for steady and unsteady, internal and external, subsonic and supersonic compressible flows. The present scheme is proved to be simple, fast and accurate compared to other meshfree methods.
Advisors
Chang, Keun-Shikresearcher장근식researcher
Description
한국과학기술원 : 항공우주공학전공,
Publisher
한국과학기술원
Issue Date
2004
Identifier
240613/325007  / 000985204
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 항공우주공학전공, 2004.8, [ vi, 65 p. ]

Keywords

COLLOCATION; POINT; MESHFREE; HYPERBOLIC; 유한요소법; 유한체적법; 차분법; UPWIND

URI
http://hdl.handle.net/10203/26311
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=240613&flag=dissertation
Appears in Collection
AE-Theses_Ph.D.(박사논문)
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