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CENTRAL SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS
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 Title & Authors
CENTRAL SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS
Shin, Su-Yeon; Hwang, Woon-Jae;
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 Abstract
The semi-discrete central scheme and central upwind scheme use Runge-Kutta (RK) time discretization. We do the Lax-Wendroff (LW) type time discretization for both schemes. We perform numerical experiments for various problems including two dimensional Riemann problems for Burgers' equation and Euler equations. The results show that the LW time discretization is more efficient in CPU time than the RK time discretization while maintaining the same order of accuracy.
 Keywords
central scheme;Lax-Wendroff type time discretization;
 Language
English
 Cited by
1.
A TREATMENT OF CONTACT DISCONTINUITY FOR CENTRAL UPWIND SCHEME BY CHANGING FLUX FUNCTIONS,;;;

Journal of the Korea Society for Industrial and Applied Mathematics, 2013. vol.17. 1, pp.29-45 crossref(new window)
 References
1.
W. Hwang and W. B. Lindquist, The 2-dimensional Riemann problem for a $2\times2$ hyperbolic conservation law. I. Isotropic media, SIAM J. Math. Anal. 34 (2002), no. 2, 341-358. crossref(new window)

2.
W. Hwang and W. B. Lindquist, The 2-dimensional problem for a $2\times2$ hyperbolic conservation law. II. Anisotropic media, SIAM J. Math. Anal. 34 (2002), no. 2, 359-384. crossref(new window)

3.
G. Jiang and E. Tadmor, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput. 19 (1998), no. 6, 1892-1917. crossref(new window)

4.
A. Kurganov, S. Noelle, and G. Petrova, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23 (2001), no. 3, 707-740. crossref(new window)

5.
A. Kurganov and G. Petrova, A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer. Math. 88 (2001), no. 4, 683-729. crossref(new window)

6.
A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000), no. 1, 241-282. crossref(new window)

7.
A. Kurganov and E. Tadmor, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer. Methods Partial Differential Equations 18 (2002), no. 5, 584-608. crossref(new window)

8.
X. Liu, S. Osher, and T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys. 115 (1994), no. 1, 200-212. crossref(new window)

9.
H. Nessyahu and E. Tadmor, Nonoscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys. 87 (1990), no. 2, 408-463. crossref(new window)

10.
J. Qiu, Hermite WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations, J. Comput. Math. 25 (2007), no. 2, 131-144.

11.
J. Qiu, WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations, J. Comput. Appl. Math. 200 (2007), no. 2, 591-605. crossref(new window)

12.
J. Qiu and C. Shu, Finite difference WENO schemes with Lax-Wendroff-Type time discretizations, SIAM J. Sci. Comput. 24 (2003), no. 6, 2185-2198. crossref(new window)

13.
D. Yoon and W. Hwang, Two-dimensional Riemann problem for Burger's equation, Bull. Korean Math. Soc. 45 (2008), no. 1, 191-205. crossref(new window)