High Order Compact Mimetic Differences and Discrete Energy Decay in 2D Wave Motions
Mimetic difference operators Div, Grad and Curl, have been constructed to provide a high order of accuracy in numerical schemes that mimic the properties of their corresponding continuum operators; hence they would be faithful to the physics. However, this faithfulness of the discrete basic operators might not be sufficient if the numerical difference scheme introduces some numerical energy increase, which would obviously result in a potentially unstable performance. We present a high order compact mimetic scheme for 2D wave motions and show that the energy of the system is also conserved in the discrete sense.
- 1.M. Abouali, J.E. Castillo, High-order compact Castillo-Grone’s operators. Report of Computational Science Research Center at San Diego State University. CSRCR02 1–13 (2012)Google Scholar
- 7.L.J. Cordova, O. Rojas, B. Otero, J.E. Castillo, Compact finite difference modeling of 2-D acoustic wave propagation. J. Comput. Appl. Math. (2015). http://www.sciencedirect.com/science/article/pii/S0377042715000618. Available online 19 February 2015
- 8.K. Hoffmann, S. Chiang, Computational Fluid Dynamics, vol. 2, 4th ed. (Engineering Education System Book, Wichita, KS, 2000)Google Scholar
- 13.R. Aberayatne, Continuum Mechanics, vol. II (Massachusetts Institute of Technology, Cambridge, MA, 2012)Google Scholar