KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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An Application of the HLLL Approximate Riemann Solver to the Shallow Water Equations

천수방정식에 대한 HLLL 근사 Riemann 해법의 적용

  • 황승용 (한국건설기술연구원 수자원.환경연구본부 하천해안연구실) ;
  • 이삼희 (한국건설기술연구원 수자원.환경연구본부 하천해안연구실)
  • Received : 2011.09.06
  • Accepted : 2011.11.24
  • Published : 2012.02.29
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Abstract

The HLLL scheme, proposed by T. Linde, determines all the wave speeds from the initial states because the middle wave is evaluated by the introduction of a generalized entropy function. The scheme is considered a genuine successor to the original HLL scheme because it is completely separated form the Roe's linearization scheme unlike the HLLE scheme and does not rely on the exact solution unlike the HLLC scheme. In this study, a numerical model was configured by the HLLL scheme with the total energy as a generalized entropy function to solve governing equations, which are the one-dimensional shallow water equations without source terms and with an additional conserved variable relating a concentration. Despite the limitations of the first order solutions, results to three cases with the exact solutions were generally accurate. The HLLL scheme appeared to be superior in comparison with the other HLL-type schemes. In particular, the scheme gave fairly accurate results in capturing the front of wetting and drying. However, it revealed shortcomings of more time-consuming calculations compared to the other schemes.

T. Linde가 제안한 HLLL 기법에서는 일반화된 엔트로피 함수의 도입으로 중앙파가 평가되므로 모든 파속이 초기 상태로부터 결정된다. HLLE 기법과 달리 Roe의 선형화 기법과 완전히 결별되고 HLLC 기법과 달리 정확해에 의존되지 않으므로 모태인 HLL 기법의 온전한 계승으로 볼 수 있다. 이 연구에서는 생성항이 없는 1차원 천수방정식에 농도와 관련된 보존변수를 추가한 지배방정식에 대해 총 에너지를 일반화된 엔트로피 함수로 두고 HLLL 기법을 적용하여 모형을 구성하였다. 정확해가 알려진 세 경우에 대해 모의한 결과, 1차 정확도 수치해의 한계에도 불구하고, 대체로 정확해와 잘 일치하였다. HLLL 기법은 그 외 HLL 형 기법에 비해 우수한 것으로 나타났다. 특히, 물이 빠져 바닥이 드러나는 경우에서 그 전선이 비교적 정확하게 포착되었다. 다만, 그 외 기법에 비해 계산 시간이 더 오래 걸리는 단점이 드러났다.

Keywords

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