Munoz-8ccmn2011 - VIII CONGRESO COLOMBIANO DE M ´ ETODOS...

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Unformatted text preview: VIII CONGRESO COLOMBIANO DE M ´ ETODOS NUM ´ ERICOS: Simulaci´on en Ciencias y Aplicaciones Industriales 8CCMN - 2011, Agosto. 10-12, 2011, Medell´ ın, Colombia c 2011 Universidad EAFIT Modelo de Lattice Boltzmann para la Simulaci´on de Campos Electro- magn´eticos Miller Mendoza 1 , 2 y Jos´e D. Mu˜noz 2 * 1 Computational Physics for Engineering Materials, Institute for Building Materials, ETH Z¨urich, Schafmattstrasse 6, HIF, CH- 8093 Z¨urich (Switzerland) 2 Grupo Simulacion de Sistemas F´ ısicos, Ceiba-Complejidad, Universidad Nacional de Colombia, Departamento de Fisica, Crr 30 # 45-03, Ed. 404, Of. 348, Bogot´a D.C., Colombia mmendozaj@unal.edu.co,jdmunozc@unal.edu.co Resumen Se presenta un modelo de lattice-Boltzmann tridimensional que reproduce en el l´ ımite cont´ ınuo las ecuaciones de Maxwell en medios materiales. El modelo utiliza un conjunto de velocidades D3Q13, con cuatro funciones de distribuci´on y cuatro vectores auxiliares asociadas a cada vector velocidad, que combinados dan los campos electromagn´eticos. El modelo permite reproducir la evoluci´on temporal de los campos en las m´as variadas situaciones: el efecto skin, la radiaci´on de un dipolo oscilante, las frecuencias de una cavidad resonante, la propagaci´on de una onda en una gu´ ıa microstrip o en una interfaz diel´ectrica, e incluso los campos en medios no lineales, todo dentro del 2 % de exactitud. El m´etodo tiene una precisi´on de segundo orden, y es diez veces m´as r´apido y usa tres veces menos memoria que los m´etodos tradicionales de diferencias finitas FDTD para campos electromagn´eticos. Adem´as, es f´acil de paralelizar en tarjetas gr´aficas (GPU), lo que lo puede acelerar entre 100 y 1000 veces. En resumen, es una alternativa valiosa y completamente diferente a los m´etodos de elementos finitos y diferencias finitas tradicionales para la simulaci´on en electrodin´amica. Palabras Clave: Simulaci´on num´erica, campos electromagn´eticos, lattice-Boltzmann Abstract Hereby we summarize a recently developed 3D lattice-Boltzmann method for the simulation of Maxwell equations in materials, and we illustrate its performance by computing the time evolution of electromagnetic fields inside a non- linear dielectric medium. The model allows for both dielectrics and conductors with realistic parameters and has computed the most diverse electromagnetic problems (including micro-strips and antennas), all with 2 % accuracy. Preliminary tests showed that it is one order of magnitude faster than the original finite-difference time-domain scheme formulated by Yee to reach the same accuracy. To illustrate the power of the new solver, we simulate the time evolution of a cylindrical electromagnetic wave through a non-linear and non-dispersive medium and the resonant modes of a cylindrical cavity filled with that medium. Our results are in excellent agreement with the analytic solutions by E.Y. Petrov and A.V. Kudrin for the same cases. The modelresults are in excellent agreement with the analytic solutions by E....
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This note was uploaded on 08/21/2011 for the course PHYS 101 taught by Professor Daniel during the Spring '11 term at Universidad Nacional de Colombia.

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Munoz-8ccmn2011 - VIII CONGRESO COLOMBIANO DE M ´ ETODOS...

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