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Stokes–Darcy Equations

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Book cover Stokes–Darcy Equations

Part of the book series: Advances in Mathematical Fluid Mechanics ((LNMFM))

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Abstract

Let \(\varOmega \subset \mathbb {R}^d\) be a Lipschitz domain split into two disjoint nonempty subdomains Ω p and Ω f which are Lipschitz, too. The index p refers to the Darcy subdomain where a porous medium is modeled, while the index f refers to the free flow domain with a Stokes model.

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Notes

  1. 1.

    Sometimes also called Beavers–Joseph–Saffman–Jones condition.

  2. 2.

    With this ψ it is \(a_{\mathrm {p}}(\varphi ,\psi ) = a_{\mathrm {p}}^R(\varphi ,\psi )\).

  3. 3.

    With this v it is .

  4. 4.

    The signs and positions of η f and η p are chosen such that the resulting system matches that in [DQV07] and [CGHW11].

  5. 5.

    For this approach it is assumed that Λ f = Λ p, see Sect. 6.6.8.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Ulrich Wilbrandt

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  1. Ulrich Wilbrandt
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Wilbrandt, U. (2019). Stokes–Darcy Equations. In: Stokes–Darcy Equations. Advances in Mathematical Fluid Mechanics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02904-3_6

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