DOI QR코드

DOI QR Code

A TREATMENT OF CONTACT DISCONTINUITY FOR CENTRAL UPWIND SCHEME BY CHANGING FLUX FUNCTIONS

  • Shin, Moungin (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
  • Shin, Suyeon (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
  • Hwang, Woonjae (DEPARTMENT OF INFORMATION AND MATHEMATICS, KOREA UNIVERSITY)
  • 투고 : 2012.06.20
  • 심사 : 2013.02.04
  • 발행 : 2013.03.25

초록

Central schemes offer a simple and versatile approach for computing approximate solutions of nonlinear systems of hyperbolic conservation laws. However, there are large numerical dissipation in case of contact discontinuity. We study semi-discrete central upwind scheme by changing flux functions to reduce the numerical dissipation and we perform numerical computations for various problems in case of contact discontinuity.

키워드

참고문헌

  1. B. Einfeldt, On godunov-type methods for gas dynamics, J. Numer. Anal. vol. 25 No. 2, 1988.
  2. G. S. Jiang and E. Tadmor, Nonoscillatory central schemes fot multidimensional hyperbolic conservation laws,SIAM J. Sci. Comput.,19, 1998, pp. 1832-1917.
  3. S. Karni, A. Kurganov and G. Petrova, A smoothness indicator for adaptive algorithms for hyperbolic systems, J. Comput. Phys. 178, 2002, pp. 323-341. https://doi.org/10.1006/jcph.2002.7024
  4. A. Kurganov and C. T. Lin, On the Reduction of Numerical Dissipation in Central-Upwind Schemes, Commun. Comput. Phys. Vol. 2, 2007, pp. 141-163.
  5. A. Kurganov, S. Noelle and G.Petrova, Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton-Jacobi equation, SIAM J. Sci. Comput.23, 2001, pp. 707-740. https://doi.org/10.1137/S1064827500373413
  6. A. Kurganov and G. Petrova, Central schemes and contact discontinuities, Math. Model. Numer. Anal. 34, 2000, pp. 1259-1275. https://doi.org/10.1051/m2an:2000126
  7. A. Kurganov, G. Petrova and B. Popov, Adaptive semi-discrete central-upwind schemes fot nonconvex hyperbolic conservation law, SIAM. J. Sci. Comput. Vol 29, No. 6, 2007, pp. 2381-2401. https://doi.org/10.1137/040614189
  8. A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations,J. Comput. Phys. 160, 2000, pp. 241-282. https://doi.org/10.1006/jcph.2000.6459
  9. P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation,Comm. Pure Appl. Math. 1954, pp. 159-193.
  10. K. A. Lie and S. Noelle, On the artificial comprssion method for second-order nonoscillatory central difference schemes for systems of cnoservation laws, SIAM J. Sci. Comput. 24, 2003, pp. 1157-1174. https://doi.org/10.1137/S1064827501392880
  11. X. D. Liu and E. Tadmor, Third order nonoscillatory central scheme for hyperbolic conservation laws, Numer. Math. vol. 79 , 1988, pp. 397-425.
  12. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys. 87, 1990, pp. 408-463. https://doi.org/10.1016/0021-9991(90)90260-8
  13. S. Shin andW. Hwang, Central schemes with Lax-Wendroff type time discretizations, Bull. Korean Math. Soc. No. 4, 2011, pp. 873-896. https://doi.org/10.4134/BKMS.2011.48.4.873

피인용 문헌

  1. Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock vol.9, pp.2, 2013, https://doi.org/10.3390/math9020138
  2. Four-Quadrant Riemann Problem for a 2×2 System II vol.9, pp.6, 2021, https://doi.org/10.3390/math9060592