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A High Order Approximation of the Two Dimensional Acoustic Wave Equation with Discontinuous Coefficients | ||
| Computational Methods for Differential Equations | ||
| مقاله 1، دوره 1، شماره 1، مهر 2013، صفحه 1-15 اصل مقاله (154.88 K) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Javad Farzi* | ||
| Sahand University Of Technology | ||
| چکیده | ||
| This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditions. We derive the required linear systems for evaluation of the coefficients of such a nonstandard method. The given novel modeling provides an overall fifth order numerical model for two dimensional acoustic wave equation with discontinuous coefficients. | ||
| کلیدواژهها | ||
| Interface methods؛ two dimensional acoustic wave equation؛ high order methods؛ Lax-Wendroff method؛ WENO؛ discontinuous coefficients؛ Jump conditions | ||
| مراجع | ||
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[1] M. Dehghan and A. Mohebbi, High Order Implicit Collocation Method for the Solution of Two-Dimensional Linear Hyperbolic Equation , Numerical Methods for Partial Differential Equations, Vol. 25, Issue 1, 232-243, 2009.
[2] J. Farzi and S. M. Hosseini, A High Order Method for the Solution of One Way Wave Equation in Heterogenous Media, Far East J. Appl. Math., Vol. 36, No. 3, 317-330, 2009.
[3] B. Gustafsson and P. Wahlund Time Compact High Order Difference Methods for Wave Propagation, 2D, . Sci. Comput., Vol. 25, pp. 195-211, 2005.
[4] R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems., Cambridge University Press, Cambridge, 2004.
[5] R. J. LeVeque, Wave Propagation Algorithms for Multidimensional Hyperbolic systems., J. comp. phys. 131,pp. 327-353, 1997.
[6] R. J. LeVeque and C. Zhang, The Immersed interface methods for wave equations with discontinuous coefficients., Wave Motion, 25, PP. 237-263, 1997.
[7] J. Qiu and C.-W. Shu, Finite difference WENO schemes with Lax-Wendroff type time discretizations., SIAM J. Sci. Comput. 24, pp. 2185-2198, 2003.
[8] C.-W. Shu, Efficient Implementation of Weighted ENO Schemes., J. Comput. Phys., 126, pp. 202-228, 1996.
[9] C. Zhang and W.W. Symes, A Forth Order Method for Acoustic Waves in Heterogenous Media, Proceedings of International Conference on Mathematical and Numerical Aspects of Wave Propagation, 1998. | ||
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