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논문 상세정보

Abstract

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.

참고문헌 (18)

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  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 
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  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 
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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 

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