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경계적분법을 이용한 2차원 영역에의 직교좌표계 구성 및 응용
Orthogonal Grid Generation in 2-D Domains via Boundary Integral Technique and Its applications
HWAHAK KONGHAK, August 1991, 29(4), 470-480(11), NONE
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Abstract
임의의 2차원 영역에 직교좌표계를 구성할 수 있는 새로운 수치적 기법을 제안하였는데 많은 공학문제의 수치해석에 응용이 기대된다. 새롭게 제안된 방법에서는 반복계산을 거치지 않고 좌표계를 직접 구성할 수 있기 때문에 거의 모든 경우에 대해 성공적으로 적용될 수 있다. 이 방법은 경계적분법과 covariant Laplace equation 방법을 조합한 것으로 다음의 두 가지 경우로 나누어 직교좌표계를 구성할 수 있다. : 1) Distortion function dmf f(ξ,η) =Π(ξ)Θ(η)와 같이 곱의 형태로 지정하거나, 2) 이웃하는 두 경계선에서 좌표계 격자점을 지정할 수 있다. 본 방법을 여러 형태의 문제에 적용하여 조사한 결과 성공에 대한 확실성이 매우 높다는 사실을 확인할 수 있었다.
A new numerical scheme, which is expected to be applied for numerical analyses of various engineering problems, is proposed for the othogonal grid generation in an arbitrary 2-D domain. The scheme is robust and non-iterative, and based on the conjunction of boundary integral technique and the covariant Laplace equation method. In the scheme, two types of problems are considered : 1)The distortion function is specified in the product form f(ξ,η)=Π(ζ)Θ(η), or 2) Boundary correspondence is specified on the two adjacent sides of the boundary. The scheme has also been tested for various application problems, and it has been confirmed that the scheme is very successful.
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