Stokes Darcy Equation (Discretized, pv)

Available identifiers

MaRDI QIDQ6674578

discrete model of Stokes-Darcy as a pressure-velocity (pv) formulation

Description

Equation (9) from the referenced 2021 arXiv manuscript by Schmalfuss et al.: Discrete model of Stokes-Darcy as a pressure-velocity (pv) formulation, to be solved for every time step.

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Defining Formula: $\left(\begin{array}{cc}\left[\begin{array}{cc}V& B\\ C& 0\end{array}\right]& \left[\begin{array}{c}B{\text{'}}_1\\ 0\end{array}\right]\\ \left[\begin{array}{cc}C{\text{'}}_1& 0\end{array}\right]& D^{\prime }\end{array}\right)\left(\begin{array}{c}\left[\begin{array}{c}{v}^{ff}\\ p^{ff}\end{array}\right]\\ p^{pm}\end{array}\right)=\left(\begin{array}{c}\left[\begin{array}{c}g\\ 0\end{array}\right]\\ 0\end{array}\right)$

$p^{ff}$ symbol represents Fluid Pressure (Free Flow)

$p^{pm}$ symbol represents Fluid Pressure (Porous Medium)

$v^{ff}$ symbol represents Fluid Velocity (Free Flow)

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