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The formal asymptotic expansion of a Darcy-Stokes coupled system
Expansión asintótica formal de un sistema Darcy-Stokes acoplado
Keywords:
Brinkman, Darcy, Stokes, porous media, multiscale coupled systems (en)Medios porosos, fractura, sistema Darcy-Stokes acoplado, Brinkmann (es)
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Using the heuristic method of formal asymptotic expansions, w analyze the order of magnitude of the diferent physical entities involved in the phenomenon of fluid exchange between geometric regions, where the velocity of the fluid flow has diferent scale. We give the modeling equations, coupling conditions and express the velocity and pressure with formal asymptotic expansions. Then we compute the averages and observe the order of magnitude of each physical effect. Finally, we deduce a Darcy-Brinkman two way coupled system of partial differential equations as the "averaged" or "homogenized" problem.
Utilizando el método heurístico de expansiones asintóticas formales se analiza el orden de magnitud de las distintas entidades físicas involucradas en el fenómeno de intercambio de fluido entre regiones geométricas, en las cuales las velocidades de flujo son de diferente orden de magnitud. Se presentan las ecuaciones de modelación, condiciones de acoplamiento y se expresan la presión y la velocidad en expansión asintótica formal. Posteriormente se calculan las medias y se observa el orden de magnitud de cada efecto físico. Finalmente, se deduce un sistema Darcy-Brinkman totalmente acoplado de ecuaciones diferenciales parciales como la forma "promediada" u "homogeneizada" del sistema original.
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