Análisis asintótico de un sistema Darcy-Stokes acoplado a través de una interfaz curva

  • Fernando A. Morales Universidad Nacional de Colombia, Escuela de Matemáticas, Medellín, Colombia.

Resumen

En el trabajo se presenta el análisis asintótico de un sistema
Darcy-Stokes acoplado a través de una interfaz curva. El sistema modela el intercambio de fluido entre un canal angosto (flujo Stokes) y un medio poroso (flujo Darcy). El canal es un dominio cilíndrico definido entre la interfaz (Τ) y una traslación paralela de dicha superficie (Τ + ε eN, ε > 0). Utilizando un cambio de variables para fijar un dominio de referencia e introduciendo dos sistemas de coordenadas, el Cartesiano canónico y el local (consistente con la geometría de la superficie), es posible encontrar la forma límite cuando el ancho del canal tiende a cero (ε→ 0). El problema límite es un sistema
acoplado con flujo Darcy en el medio poroso y flujo Brinkman en la interfaz (Τ).

Palabras clave: medio poroso, interfaces curvas, sistema Darcy-Stokes, sistema Darcy-Brinkman

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Citas

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Publicado
2019-07-29