한국항공우주학회지 (Journal of the Korean Society for Aeronautical & Space Sciences)

  • 제32권9호
  • /
  • Pages.1-11
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  • 2004
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  • 1225-1348(pISSN)
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  • 2287-6871(eISSN)
한국항공우주학회 (The Korean Society for Aeronautical and Space Sciences)
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비정렬 격자계에서 LU Implicit Scheme의 수렴성 및 안정성 해석 : Part I-오일러 방정식

Convergence and Stability Analysis of LU Scheme on Unstructured Meshes: Part I - Euler Equations

  • 김주성 (한국과학기술원 항공우주공학과 대학원) ;
  • 권오준 (한국과학기술원 항공우주공학과)
  • 발행 : 2004.11.01
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초록

본 연구에서는 비정렬 격자계에서 가장 많이 쓰이는 근사 해법 중의 하나인 LU 기법의 오일러 방정식에 대한 수렴성 및 안정성에 관한 연구를 수행하였다. 적절한 스칼라 모델 방정식을 사용하여 LU기법이 갖는 고유한 특성에 관해서 해석적으로 논의하였으며, 이를 system of equations 형태인 오일러 방정식으로 확장 해석하였다. 해석 결과 LU 기법의 수렴성 및 안정성은 격자 종횡비와 연관된 특별한 독립변수의 조합으로 표현되며, 이러한 독립 변수의 조합을 사용하여 어떠한 종횡비의 격자에 대해시도 수렴성 및 안정성의 저하 현상이 발생되지 않음을 보였다.

A comprehensive study has been made for the investigation of the convergence and stability characteristics of the LU scheme for solving the Euler equations on unstructured meshes. The von Neumann stability analysis technique was initially applied to a scalar model equation, and then the analysis was extended to the Euler equations. The results indicated that the convergence rate is governed by a specific combination of flow parameters. Based on this insight, it was shown that the LU scheme does not suffer any convergence deterioration at all grid aspect ratios, as long as the local time step is defined using an appropriate parameter combination.

키워드

참고문헌

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