Numerical methods and fuzzy parameters: an environmental impact assessment in aquatic systems

Poletti, Elaine Cristina Catapani; Meyer, John-Jules

doi:10.1007/s40314-015-0299-z

Cited by 1 publication

(2 citation statements)

References 19 publications

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“…Either because of lack of information about the true values for the parameters involved or in order to facilitate the numerical methods involved. For example, in some cases where the outward flux must be null, condition (2.10) is used instead of (2.8) [5,7,8,9,10,12,13,14,16,17,18,19,20,21,23]. In others, where there is a partial flux on the boundary, condition (2.16) is used instead of (2.13), [8,10,14,20].…”

Section: Resultsmentioning

confidence: 99%

“…The main purpose of these works is to obtain models based on advection-diffusion equations or systems and numerical approximations to their solutions, generally by means of the Finite Elements or Finite Differences methods. Some works analyzed pollutant dispersal, either in rivers [5], in the sea [6], lakes in two [7] and three dimensions [8], air [9], or mixed [10]. In [11], steady-state air pollution is modeled.…”

Section: Introductionmentioning

confidence: 99%

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

Miyaoka

Meyer

Souza

2017

Tend. Mat. Apl. Comput.

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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.

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