Vol. 12

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2010-04-08

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

By Narendra Deore and Avijit Chatterjee
Progress In Electromagnetics Research M, Vol. 12, 1-15, 2010
doi:10.2528/PIERM10022003

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.

Citation


Narendra Deore and Avijit Chatterjee, "A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering," Progress In Electromagnetics Research M, Vol. 12, 1-15, 2010.
doi:10.2528/PIERM10022003
http://jpier.org/PIERM/pier.php?paper=10022003

References


    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

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

    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

    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

    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.

    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.

    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

    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

    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

    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

    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.

    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

    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

    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.

    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

    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