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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.8 n.2 México Oct./Dec. 2004

 

Resumen de tesis doctoral

 

Accurate Flexible Numerical Boundary Conditions for Multidimensional Transport and Diffusion

 

Precisas Flexibles Condiciones de Frontera Numéricas para el Transporte y Difusión Multidimensional

 

Graduated: Dr. Denis Filatov
Centre for Computing Research (CIC),
National Polytechnic Institute (IPN),
Av. Juan de Dios Batiz s/n,
C.P. 07738, Mexico, D.F.

E–mail: denisfilatov@mail.ru

Advisor: Prof. Dr. Mikhail Alexandrov
Centre for Computing Research (CIC),
National Polytechnic Institute (IPN),
Av. Juan de Dios Batiz s/n,
C.P. 07738, Mexico, D.F.

E–mail: dynerl950@mail.ru

Co–Advisor: Prof. Dr. Sc. Mikhail Yudin
Moscow State Geological Prospecting University (MGRI–MGGU),
23 Miklukho–Maklaya st, 117997, Moscow, Russia

E–mail: judin@msgpa.ru

 

Graduated on: January 20, 2004

 

Abstract

A method for numerical solution to the advection–diffusion–reaction equation in unbounded domains is developed. The method is based on the concept of artificial boundary conditions (ABCs), and employs the techniques of time and dimensional splitting of the partial differential equation coupled with domain decomposition of the original infinite space. The essentials of the method is that it is applicable for solving a wide class of mass transportation problems in domain of drastically complex geometries, realisable from the computation standpoint, and provides a highly accurate solution at minimal computational efforts.

Keywords: Artificial (numerical) boundary conditions, advection–diffusion–reaction equation, splitting, domain decomposition.

 

Resumen

Se desarrolla un método para la solución numérica de la ecuación de advección–difusión–reacción en dominios infinitos. El método se basa en el concepto de condiciones de frontera artificiales (CFAs), y utiliza las técnicas de escisión del operador por tiempo y por espacio junto con la de descomposición de dominio para el espacio original infinito. Los esenciales del método son lo que es aplicable para dar solución a una amplia clase de los problemas de transporte de masa en dominios de la geometría demasiado compleja, realizable desde el punto de vista numérico, y además proporciona una alta precisión de la solución con mínimos esfuerzos computacionales.

Palabras clave: Condiciones de frontera artificiales (numéricas), ecuación de advección–difusión–reacción, escisión del operador, descomposición de dominio.

 

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