A General Boundary Condition with Linear Flux for Advection-Diffusion Models

Tiago Yuzo Miyaoka, João Frederico da Costa Azevedo Meyer, Juliana Marta Rodrigues de Souza

Abstract


Advection-diffusion equations are widely used in modeling a diverse range of problems. These mathematical models consist in a partial differential equation or system with initial and boundary conditions, which depend on the phenomena being studied. In the modeling, boundary conditions may be neglected and unnecessarily simplified, or even misunderstood, causing a model not to reflect the reality adequately, making qualitative and/or quantitative analyses more difficult. In this work we derive a general linear flux dependent boundary condition for advection-diffusion problems and show that it generates all possible boundary conditions, according to the outward flux on the boundary. This is done through an integral formulation, analyzing the total mass of the system. We illustrate the exposed cases with applications willing to clarify their meanings. Numerical simulations, by means of the Finite Difference Method, are used in order to exemplify the different boundary conditions' impact, making it possible to quantify the flux along the boundary. With qualitative and quantitative analysis, this work can be useful to researchers and students working on mathematical models with advection-diffusion equations.

Keywords


Boundary conditions; Partial differential equations; Mathematical models; Computer simulation

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DOI: http://dx.doi.org/10.5540/tema.2017.018.02.0253

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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