# The Solution of Two Dimensional and Time Dependent Burger Equations Using Finite Difference Method

## Authors

• Mohammad Vaghefi Assistant Professor of Hydraulic Structure, Civil Engineering Department, Persian Gulf University, Bushehr, Iran.
• Sam Boveiri Master of Science, Department of Civil Engineering, Pardis Branch, Persian Gulf University, Bushehr, Iran
• Ali Reza Fiouz Assistant Professor of Structures, Department of Civil Engineering, Persian Gulf University, Bushehr, Iran

## Keywords:

Burger Equation, Finite Difference, Newton-Raphson Method, Velocity Distribution

## Abstract

There is a differential equation governing all engineering phenomena. For some of these phenomenas, there are mathematical models that define the behavior pattern of that phenomena in different conditions. The equation we used in this study was the two dimensional and time dependent burger equation. This equation is discontinued through using finite differentiation and solved using newton Robinson technique in Matlab program. Then sensitivity analysis has been performed on time passage and their effect on sedimentation velocity have been studied and analyzed. The results that showed that in the most of times, the skewness diagrams of length and depth velocity in depth direction to is to the left which shows the maximum velocity of falling particle at the time of study and near the bed.

## References

Abdou, M. A., and Soliman, A. A., â€œVariational iteration method for solving Burger's and coupled Burger's equationsâ€, Journal of Computational and Applied Mathematics, Vol. 181, No. 2, pp. 245-251, 2005.

Wazwaz, A. M., â€œMultiple kink solutions for M-component Burgers equations in (1+1)-dimensions and (2+1)-dimensionsâ€, Applied Mathematics and Computation, Vol. 217, No. 7, pp. 3564-3570, 2010.

Wei, G. W., and Gu, Y., â€œConjugate filter approach for solving Burgersâ€™ equationâ€, Journal of Computational and Applied mathematics, Vol. 149, No. 2, pp. 439-456, 2002.

DaÄŸ, Ä°., CanÄ±var, A., and Åžahin, A., â€œTaylorâ€“Galerkin and Taylor-collocation methods for the numerical solutions of Burgersâ€™ equation using B-splinesâ€, Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 7, pp. 2696-2708, 2011.

Shao, L., Feng, X., and He, Y., â€œThe local discontinuous Galerkin finite element method for Burgerâ€™s equation. Mathematical and Computer Modellingâ€, Vol. 54, No. 11, pp. 2943-2954, 2011.

Soliman, A. A., â€œThe Modified Extended Tanh-function method for solving Burgers-type equationsâ€, Physica A: Statistical Mechanics and its Applications, Vol. 361, No. 2, pp. 394-404, 2006.

Haq, S., and Uddin, M., â€œA mesh-free method for the numerical solution of the KdVâ€“Burgers equationâ€, Applied Mathematical Modelling, Vol. 33, No. 8, pp. 3442-3449, 2009.

Mittal, R. C., and Arora, G., â€œNumerical solution of the coupled viscous Burgersâ€™ equationâ€, Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 3, pp. 1304-1313, 2011.

Vaghefi, M., Rahideh, H., khaksar, A., and Golbahar Haghighi, M.R., â€œDistributed approximating Functional approach to Burgers' equation using differential quadratuve methodâ€, Journal of Applied Sciences and Environmental Management, Vol. 16, No. 1, pp. 5-10, 2012.

Hongyan, Z., and Hongqing, Z., â€œNew ration solitary wave Solutions of (2+1)-dimensional Burger's equationâ€, Nonlinear Analysis, Vol. 66, No. 34, pp. 2264-2273, 2007.

Feng, S., Liang, P., and Jun, Z., â€œNew Exact solution to (3+1) Dimensional Burger's Equationâ€, Communications in Theoretical Physics (Beijing, China), Vol. 42, No. 26, pp. 49-50, 2004.

Dai, C. Q., and Wang, Y. Y., â€œNew exact solutions of the (3+1)-dimensional Burgers systemâ€, Physics Letters A, Vol. 373, No. 2, pp. 181-187, 2009.

Christou, M. A., Ivanova, N. M., and Sophocleous, C., â€œSimilarity reductions of the (1+3)-dimensional Burgers equationâ€, Applied Mathematics and Computation, Vol. 210, No. 1, pp. 87-99, 2009.

Christou, M. A., and Sophocleous, C., â€œNumerical similarity reductions of the (1+3)-dimensional Burgers equationâ€, Applied Mathematics and Computation, Vol. 217, No. 18, pp. 7455-7461, 2011.

Abdel Rady, A. S., Osman, E. S., and Khalfallah, M., â€œMulti-soliton solution, rational solution of the Boussinesqâ€“Burgers equationsâ€, Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 5, pp. 1172-1176, 2010.

Dehghan, M., Nematisaray, B., and Lakestani, M., â€œThree Methods based on the interpolation scaling Functions and the mined colloction Finite Difference schemes for the numerical solution of the nonlinear generalized Burger's-Huxley equationâ€, Mathematical and computer Modelling, Vol. 55, No. 21, pp. 1129-1142, 2012.

Zhao, T., Li, C., Zang, Z., and Wu, Y., â€œChebyshevâ€“Legendre pseudo-spectral method for the generalised Burgersâ€“Fisher equationâ€, Applied Mathematical Modelling, Vol. 36, No. 3, pp. 1046-1056, 2012.

Korpusov, M. O., â€œOn the blow-up of solutions of the Benjaminâ€“Bonaâ€“Mahonyâ€“Burgers and Rosenauâ€“Burgers equationsâ€, Nonlinear Analysis: Theory, Methods & Applications, Vol. 75, No. 4, pp. 1737-1743, 2012.

Haq, S., Hussain, A., and Uddin, M., â€œOn the numerical solution of nonlinear Burgersâ€™-type equations using meshless method of linesâ€, Applied Mathematics and Computation, Vol. 218, No. 11, pp. 6280-6290.

2014-12-15

## How to Cite

Vaghefi, M., Boveiri, S., & Fiouz, A. R. (2014). The Solution of Two Dimensional and Time Dependent Burger Equations Using Finite Difference Method. Asian Journal of Engineering and Technology, 2(6). Retrieved from https://ajouronline.com/index.php/AJET/article/view/1852

Articles