“Influencia del término difusivo en el modelamiento de transporte de masa usando la ecuación de convección difusión no lineal”
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Date
2024
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Universidad Nacional de Trujillo
Abstract
En este trabajo se emplea la ecuación de Convección-Difusión no lineal en 1D y 2D para
modelar el proceso de convectivo difusivo de la masa, donde las partículas o la energía se
transforman dentro de un sistema físico debido a dos procesos: la difusión y la convección.
El coeficiente de difusión se consideró espacialmente constante y solamente dependiente de
la naturaleza de la sustancia. La idea y los esquemas numéricos se aplicaron a un dominio
en el plano XY de lado 1, donde se aprecia la distribución de la masa.
Se ha usado condiciones de frontera, con el fin de hacer un corte en dicha frontera para la
modelación. El programa computacional realizado permite mover la fuente de masa
contaminante a cualquier punto del domino y ver su distribución en tiempo real, además se
puede añadir otras fuentes de masa contaminante y observar el proceso convectivo difusivo
de este.
En el caso lineal a medida que el valor de la concentración de masa se reduce en el tiempo,
se aprecia una ralentización de la velocidad de la onda.
En el caso no lineal en 1D y 2D observamos como el termino difusivo se implica en la
formación de ondas de choque en la solución, generando una discontinuidad o salto; en
ausencia este término difusivo la formación de la onda de choque es inminente. (capitulo
III). La modelación también permitió obtener el resultado sobre la generación de una zona
de rarefacción, donde las ondas no se juntan y una zona donde las ondas se juntan unas a
otras o zona de comprensión. Pudimos observar que el termino difusivo es crucial para
generar una zona de compresión de ondas más agudo, como una cuña que se desplaza en la
dirección X.
In this work, the nonlinear Convection-Diffusion equation is used in 1D and 2D to model the diffusive convective process of mass, where particles or energy are transformed within a physical system due to two processes: diffusion and convection. The diffusion coefficient was considered spatially constant and only dependent on the nature of the substance. The idea and the numerical schemes were applied to a domain in the XY plane of side 1, where the mass distribution is appreciated. Border conditions have been used, in order to make a cut on said border for modeling. The computer program carried out allows moving the polluting mass source to any point of the domain and seeing its distribution in real time, in addition other sources of polluting mass can be added and observing its convective diffusive process. In the linear case, as the value of the mass concentration decreases over time, a slowing down of the wave speed is observed. In the non-linear case in 1D and 2D, we observe how the diffusive term is involved in the formation of shock waves in the solution, generating a discontinuity or jump; in the absence of this diffusive term the formation of the shock wave is imminent. (Chapter III). The modeling also allowed obtaining the result on the generation of a rarefaction zone, where the waves do not come together and an area where the waves join each other or compression zone. We were able to observe that the diffusive term is crucial to generate a sharper wave compression zone, like a wedge that moves in the X direction.
In this work, the nonlinear Convection-Diffusion equation is used in 1D and 2D to model the diffusive convective process of mass, where particles or energy are transformed within a physical system due to two processes: diffusion and convection. The diffusion coefficient was considered spatially constant and only dependent on the nature of the substance. The idea and the numerical schemes were applied to a domain in the XY plane of side 1, where the mass distribution is appreciated. Border conditions have been used, in order to make a cut on said border for modeling. The computer program carried out allows moving the polluting mass source to any point of the domain and seeing its distribution in real time, in addition other sources of polluting mass can be added and observing its convective diffusive process. In the linear case, as the value of the mass concentration decreases over time, a slowing down of the wave speed is observed. In the non-linear case in 1D and 2D, we observe how the diffusive term is involved in the formation of shock waves in the solution, generating a discontinuity or jump; in the absence of this diffusive term the formation of the shock wave is imminent. (Chapter III). The modeling also allowed obtaining the result on the generation of a rarefaction zone, where the waves do not come together and an area where the waves join each other or compression zone. We were able to observe that the diffusive term is crucial to generate a sharper wave compression zone, like a wedge that moves in the X direction.
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Keywords
Convección, Difusión, Diferencias finitas, Condiciones de frontera de
Newman