본문 바로가기
HOME> 논문 > 논문 검색상세

논문 상세정보

Bulletin of the Korean Mathematical Society = 대한수학회보 v.45 no.1, 2008년, pp.191 - 205   피인용횟수: 2

TWO-DIMENSIONAL RIEMANN PROBLEM FOR BURGERS' EQUATION

Yoon, Dae-Ki   (DEPARTMENT OF MATHEMATICS KOREA UNIVERSITYUU0000159  ); Hwang, Woon-Jae   (DEPARTMENT OF INFORMATION AND MATHEMATICS KOREA UNIVERSITYUU0000159  );
  • 초록

    In this paper, we construct the analytic solutions and numerical solutions for a two-dimensional Riemann problem for Burgers' equation. In order to construct the analytic solution, we use the characteristic analysis with the shock and rarefaction base points. We apply the composite scheme suggested by Liska and Wendroff to compute numerical solutions. The result is coincident with our analytic solution. This demonstrates that the composite scheme works pretty well for Burgers' equation despite of its simplicity.


  • 주제어

    2D Riemann problem .   conservation laws .   Burgers' equation .   composite scheme.  

  • 참고문헌 (18)

    1. T. Chang, G. Chen, and S. Yang, On the 2-D Riemann problem for the compressible Euler equations. I. Interaction of shocks and rarefaction waves, Discrete Contin. Dynam. Systems 1 (1995), no. 4, 555-584 
    2. T. Chang and L. Hsiao, The Riemann Problem and Interaction of Waves in Gas Dynamics, Pitman Monographs and Surveys in Pure and Applied Mathematics, 41. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989 
    3. G. Chen, D. Li, and D. Tan, Structure of Riemann solutions for 2-dimensional scalar conservation laws, J. Differential Equations 127 (1996), no. 1, 124-147 
    4. J. Guckenheimer, Shocks and rarefactions in two space dimensions, Arch. Rational Mech. Anal. 59 (1975), no. 3, 281-291 
    5. W. Hwang, The 2-dimensional Riemann problem, J. Inst. Sci. Tech. Korea University 12 (2004), 29-34 
    6. W. Hwang and W. B. Lindquist, The 2-dimensional Riemann problem for a 2 $\times$ 2 hyperbolic conservation law. I. Isotropic media, SIAM J. Math. Anal. 34 (2002), no. 2, 341-358 
    7. W. Hwang and W. B. Lindquist, The 2-dimensional Riemann problem for a 2 $\times$ 2 hyperbolic conservation law. II. Anisotropic media, SIAM J. Math. Anal. 34 (2002), no. 2, 359-384 
    8. W. B. Lindquist, The scalar Riemann problem in two spatial dimensions: piecewise smoothness of solutions and its breakdown, SIAM J. Math. Anal. 17 (1986), no. 5, 1178-1197 
    9. W. B. Lindquist, Construction of solutions for two-dimensional Riemann problems, Hyperbolic partial differential equations, III. Comput. Math. Appl. Part A 12 (1986), no. 4-5, 615-630 
    10. R. Liska and B. Wendroff, Composite schemes for conservation laws, SIAM J. Numer. Anal. 35 (1998), no. 6, 2250-2271 
    11. C. Schulz-Rinne, Classification of the Riemann problem for two-dimensional gas dynamics, SIAM J. Math. Anal. 24 (1993), no. 1, 76-88 
    12. C. Schulz-Rinne, J. Collins, and H. Glaz, Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comput. 14 (1993), no. 6, 1394-1414 
    13. D. Wagner, The Riemann problem in two space dimensions for a single conservation law, SIAM J. Math. Anal. 14 (1983), no. 3, 534-559 
    14. T. Zhang and G. Chen, Some fundamental concepts about system of two spatial dimensional conservation laws, Acta Math. Sci. (English Ed.) 6 (1986), no. 4, 463-474 
    15. P. Zhang and T. Zhang, Generalized characteristic analysis and Guckenheimer structure, J. Differential Equations 152 (1999), no. 2, 409-430 
    16. R. Liska and B. Wendroff, Two dimensional shallow water equations by composite schemes, Int. J. Numer. Meth. Fluids 30 (1999), 461-479 
    17. T. Zhang and Y. Zheng, Two-dimensional Riemann problem for a single conservation law, Trans. Amer. Math. Soc. 312 (1989), no. 2, 589-619 
    18. T. Zhang and Y. Zheng, Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems, SIAM J. Math. Anal. 21 (1990), no. 3, 593-630 
  • 이 논문을 인용한 문헌 (2)

    1. 2011. "" Bulletin of the Korean Mathematical Society = 대한수학회보, 48(4): 873~896     
    2. 2013. "" Bulletin of the Korean Mathematical Society = 대한수학회보, 50(1): 201~216     

 활용도 분석

  • 상세보기

    amChart 영역
  • 원문보기

    amChart 영역

원문보기

무료다운로드
유료다운로드
  • 원문이 없습니다.

유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.

원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.

NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.

이 논문과 함께 출판된 논문 + 더보기