Un nuevo esquema iterativo robusto y eficiente para un problema parabólico no lineal degenerado

  • Guillermo A. Albuja Proaño Universidad Central del Ecuador, UCE, Facultad de Ciencias, Ciudadela Universitaria, Quito-Ecuador
  • Iván C. Naula Reina Universidad Central del Ecuador, UCE, Facultad de Ciencias, Ciudadela Universitaria, Quito-Ecuador,

Resumen

El flujo de agua a través del suelo esta modelado matemáticamente por la ecuación de Richards. Esta ecuación doblemente no lineal degenerada, es difícil de resolver, más aun  la no linealidad y la degeneración hacen que el diseño de esquemas numéricos para este problema sea una tarea desafiante.  Según la literatura los métodos implícitos son los que dan mejores resultados ya que los esquemas obtenidos permiten simular el problema degenerado sin embargo estos producen problemas no lineales que deben ser resueltos mediante métodos de linealización.
En esta investigación se desarrolla un nuevo esquema numérico de linealización de la ecuación de Richards. Se usa un esquema de Euler totalmente implícito para discretizar el tiempo y elementos finitos para discretizar el espacio, sin embargo, estos esquemas deberían funcionar para cualesquier discretización espacial escogida. Se consiguió un esquema mas robusto y más rápido (en lo que a número de iteraciones y tiempo total de máquina empleado se refiere) que los ya existentes.

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Publicado
2019-12-27
Sección
Articulos