Numerical Simulation of a Class of Nonlinear Wave Equations by Lattice Boltzmann Method
Tóm tắt
Từ khóa
Tài liệu tham khảo
Pozar, D.: Microwave Engineering. Addison-Wesley, NewYork (1990)
Mohebbi, A., Dehghan, M.: High order compact solution of the one-space-dimensional linear hyperbolic equation. Numer Methods Partial Differ. Equ. 24(5), 1222–1235 (2008)
Jeffrey, A.: Applied Partial Differential Equations. Academic Press, NewYork (2002)
Dehghan, M., Ghesmati, A.: Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method. Eng. Anal. Bound. Elem. 34(1), 51–59 (2010)
Mohanty, R.K.: New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations. Int. J. Comput. Math. 86(12), 2061–2071 (2009)
Pascal, H.: Pressure wave propagation in a fluid flowing through a porous medium and problems related to interpretation of Stoneley’s wave attenuation in a coustical well logging. Int. J. Eng. Sci. 24, 1553–1570 (1986)
Bohme, G.: Non-Newtonian fluid mechanics. North-Holland, NewYork (1987)
Evans, D.J., Bulut, H.: The numerical solution of the telegraph equation by the alternating group explicit method. Int. J. Comput. Math. 80, 1289–1297 (2003)
Jordan, P.M., Meyer, M.R., Puri, A.: Causal implications of viscous damping in compressible fluid flows. Phys. Rev. E 62, 7918–7926 (2000)
Scott, A.: Nonlinear Science: Emergence and Dynamics of Coherent Structures. Oxford University Press, Oxford (2003)
Dauxois, T., Peyrard, M.: Physics of Solitons. Cambridge University Press, Cambridge (2006)
Liu, L., Liu, H.: Compact difference schemes for solving telegraphic equations with Neumann boundary conditions. Appl. Math. Comput. 219(19), 10112–10121 (2013)
Rashidinia, J., Mohammadi, R.: Tension spline approach for the numerical solution of nonlinear Klein–Gordon equation. Comput. Phys. Commun. 181, 78–91 (2010)
Rashidinia, J., Mohammadi, R.: Tension spline solution of nonlinear sine-Gordon equation. Numer Algorithms 56, 129–142 (2011)
Mohebbi, A., Dehghan, M.: High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods. Math. Comput. Modell. 51, 537–549 (2010)
Moghaderi, H., Dehghan, M.: A multigrid compact finite differencemethod for solving the one-dimensional nonlinear sine-Gordon equation. Math. Methods Appl. Sci. 38, 3901–3922 (2015)
Mohebbi, A., Dehghan, M.: High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods. Math. Comput. Modell. 51, 537–549 (2010)
Mittal, R.C., Bhatia, R.: Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic B-spline collocation method. Appl. Math. Comput. 220, 496–506 (2013)
Rashidinia, J., Ghasemia, M., Jalilian, R.: Numerical solution of the nonlinear Klein–Gordon equation. J. Comput. Appl. Math. 233, 1866–1878 (2010)
Sharifi, S., Rashidinia, J.: Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method. Appl. Math. Comput. 281, 28–38 (2016)
Liu, W., Wu, B., Sun, J.: Space–time spectral collocation method for the one-dimensional sine-Gordon equation. Numer. Methods Partial Differ. Equ. 31, 670–690 (2015)
Shao, W., Wu, X.: The numerical solution of the nonlinear Klein–Gordon and Sine–Gordon equations using the Chebyshev tau meshless method. Comput. Phys. Commun. 185, 1399–1409 (2014)
Khuri, S.A., Sayfy, A.: A spline collocation approach for the numerical solution of a generalized nonlinear Klein–Gordon equation. Appl. Math. Comput. 216, 1047–1056 (2010)
Dawson, S.P., Chen, S., Doolen, G.D.: Lattice Boltzmann computations for reaction–diffusion equations. J. Chem. Phys. 2, 1514–1523 (1993)
Zhang, J., Yan, G.: A lattice Boltzmann model for the Korteweg–de Vries equation with two conservation laws. Comput. Phys. Commun. 180, 1054–1062 (2009)
Duan, Y., Liu, R.: Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation. J. Comput. Appl. Math. 206, 432–439 (2007)
Shi, B., Guo, Z.: Lattice Boltzmann model for nonlinear convection–diffusion equations. Phy. Rev. E 79, 016701 (2009)
Lai, H., Ma, C.: Lattice Boltzmann modei for generalized nonlinear wave equation. Phys. Rev. E 84, 046708 (2011)
Duan, Y., Kong, L.: A lattice Boitzmann model for the generalized Burgers–Hulexly equation. Phys. A 391, 625–632 (2012)
Duan, Y., Chen, X., Kong, L.: Lattice Boltzmann model for the compound Burgers–Korteweg–de Vries equation. Chin. J. Comput. Phys. 32(6), 639–648 (2015)
Higuera, F., Succi, S., Benzi, R.: Lattice gas dynamics with enhanced collisions. Euro. Phys. Lett. 9, 345–349 (1989)
Benzi, R., Succi, S., Vergassola, M.: The lattice Boltzmann equation: theory and applications. Phys. Rep. 222(3), 145–197 (1992)
Qian, Y., Succi, S., Orszag, S.: Recent advances in lattice Boltzmann computing. Annu. Rev. Comput. Phys. 3, 195–242 (1995)
Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998)
Luo. L.: The lattice-gas and lattice Boltzmann methods: past, present and future. In: Proceedings of International Conference on Applied Computational Fluid Dynamics. October, China, Beijing, pp. 52-83 (2000)
Bhatnagar, P., Gross, E., Krook, M.: A model for collision process in gas. I: small amplitude processed in charged and neutral one component system. Phys. Rev. 94, 511–525 (1954)
Dehghan, M., Shokri, A.: A numerical method for solving the hyperbolic telegraph equation. Numer. Methods Partial Differ. Equ. 24, 1080–1093 (2008)
Jang, T.S.: A new solution procedure for the nonlinear telegraph equation. Commun. Nonlinear Sci. Numer. Simul. 29, 307–326 (2015)
He, B., Meng, Q., Long, Y., Rui, W.: New exact solutions of the double sine-Gordon equation using symbolic computations. Appl. Math. Comput. 186, 1334–1346 (2007)
