volume | PIER Journals

Abstract

A cell-vertex based finite volume scheme is used to solve the time-dependentMaxwell's equations and predict electromagnetic scattering from perfectly conducting bodies. The scheme is based on the cell-vertex finite volume integration method, originally proposed by Ni[1], for solution of the two dimensional unsteady Euler equations of gas dynamics. The resulting solution is second-order accurate in space and time, and requires cell based fluctuations to be appropriately distributed to the state vector stored at cell vertices at each time step. Results are presented for two-dimensional canonical shapes and complex three dimensional geometries. Unlike in gas dynamics, no user defined numerical damping is required in this novel cell-vertex based finite volume integration scheme when applied to the time-domain Maxwell's equations.

1. Ni, R.-H., "A multiple-grid scheme for solving the Euler equations," AIAA Journal, Vol. 20, 1565-1571, 1982.
doi:10.2514/3.51220 Google Scholar

2. Shankar, V., "A gigaflop performance algorithm for solving Maxwell's equations of electromagnetics," AIAA Paper, 91-1578, Jun. 1998. Google Scholar

3. Yee, K., "Numerical solutions of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, 302-307, 1966.
doi:10.1109/TAP.1966.1138693 Google Scholar

4. Shang, J. S., "Shared knowledge in computational fluid dynamics, electromagnetics, and magneto-aerodynamics," Progress in Aerospace Sciences, Vol. 38, No. 6, 449-467, 2002.
doi:10.1016/S0376-0421(02)00028-3 Google Scholar

5. Roe, P. L., "Fluctuations and signals --- A framework for numerical evolution problems," Numerical Methods in Fluid Dynamics, K. W. Morton and M. J. Baines (eds.), Academic Press, 219-257, 1982. Google Scholar

6. Hall, M. G., "Cell-vertex multigrid schemes for solution of the Euler equations," Numerical Methods for Fluid Dynamics II, K. W. Morton and M. J. Baines (eds.), 303{345, Clarendon Press, Oxford, 1985. Google Scholar

7. Zhu, Y. and J. J. Chattot, "Computation of the scattering of TM plane waves from a perfectly conducting square --- Comparisons of Yee's algorithm, Lax-Wendroff method and Ni's scheme," Antennas and Propagation Society International Symposium, Vol. 1, 338-341, 1992.

8. Chatterjee, A. and A. Shrimal, "Essentially nonoscillatory finite volume scheme for electromagnetic scattering by thin dielectric coatings," AIAA Journal, Vol. 42, No. 2, 361-365, 2004.
doi:10.2514/1.553 Google Scholar

9. Chatterjee, A. and R. S. Myong, "Efficient implementation of higher-order finite volume time-domain method for electrically large scatterers," Progress In Electromagnetics Research B, Vol. 17, 233-254, 2009.
doi:10.2528/PIERB09073102 Google Scholar

10. Koeck, C., "Computation of three-dimensional flow using the Euler equations and a multiple-grid scheme," International Journal for Numerical Methods in Fluids, Vol. 5, 483-500, 1985.
doi:10.1002/fld.1650050507 Google Scholar

11. Shankar, V., W. F. Hall, and A. H. Mohammadin, "A time-domain differential solver for electromagnetic scattering problems," Proceedings of the IEEE, Vol. 77, No. 5, 709-721, 1989.
doi:10.1109/5.32061 Google Scholar

12. Ni, R. H. and J. C. Bogoian, "Prediction of 3-D multistage turbine flow field using a multiple-grid euler solver," AIAA Paper, 1-9, 890203, Jan. 1989. Google Scholar

13. French, A. D., "Solution of the Euler equations on cartesian grids," Applied Numerical Mathematics, Vol. 49, 367-379, 2004.
doi:10.1016/j.apnum.2003.12.014 Google Scholar

14. Woo, A. C., H. T. G. Wang, M. J. Schuh, and M. L. Sanders, "Benchmark radar targets for the validation of computational electromagnetics programs," IEEE Antennas and Propagation Society Magazine, Vol. 35, No. 1, 84-89, 1993.
doi:10.1109/74.210840 Google Scholar

15. Chatterjee, A. and S. P. Koruthu, "Characteristic based FVTD scheme for predicting electromagnetic scattering from aerospace configurations ," Journal of the Aeronautical Society of India, Vol. 52, No. 3, 195-205, 2000. Google Scholar

16. Leveque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, UK, 2002.

17. Rossmanith, J. A., "A wave propagation method for hyperbolic systems on the sphere," Journal of Computational Physics, Vol. 213, 629-658, 2006.
doi:10.1016/j.jcp.2005.08.027 Google Scholar

18. Chakrabartty, S. K., K. Dhanalakshmi, and J. S. Mathur, "Computation of three dimensional transonic flow using a cell vertex finite volume method for the Euler equations," Acta Mechanica, Vol. 115, 161-177, 1996.
doi:10.1007/BF01187436 Google Scholar

Dr. Narendra Deore

Prof. Avijit Chatterjee