This benchmark deals with fluid flow through an open parallelplate channel. The figure below gives a pictorial view of the considered scenario.
The model parameters used in the simulation are summarized in the table below.
Parameter  Unit  Value 

Hydraulic pressure at the inlet $P_{\mathrm{in}}$  Pa  200039.8 
Hydraulic pressure at the outlet $P_{\mathrm{out}}$  Pa  200000 
Fluid dynamic viscosity $\mu$  Pa$\cdot$s  5e3 
The fluid motion in the parallelplate channel can be described by the Stokes equation. To close the system of equations, the continuity equation for incompressible and steadystate flow is applied. The governing equations of incompressible flow in the entire domain are given as (Yuan et al., 2016)
$$ \begin{equation} \nabla p  \mu \Delta \mathbf{v} = \mathbf{f}, \end{equation}$$\begin{equation} \nabla \cdot \mathbf{v} = 0. \end{equation}
Figure 2(a) shows the hydraulic pressure profile through the parallelplate flow channel, wherein the pressure drop is linearly distributed. Figure 2(b) gives the transverse velocity component profile over the crosssection of the plane flow channel which shows a parabolic shape. The transverse velocity component reaches a maximum value of 0.004975 m/s at the center which conforms to the value obtained from the analytical solution of the transverse velocity component. The analytical solution of the velocity is given as (Sarkar et al., 2004)
$$ \begin{equation} v \left(y\right) = \frac{1}{2\mu} \frac{P_{\mathrm{in}}  P_{\mathrm{out}}}{l} y \left( b  y\right). \end{equation}$$Sarkar, S., Toksoz, M. N., & Burns, D. R. (2004). Fluid flow modeling in fractures. Massachusetts Institute of Technology. Earth Resources Laboratory.
Yuan, T., Ning, Y., & Qin, G. (2016). Numerical modeling and simulation of coupled processes of mineral dissolution and fluid flow in fractured carbonate formations. Transport in Porous Media, 114(3), 747775.
This article was written by Renchao Lu, Dmitri Naumov. If you are missing something or you find an error please let us know.
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Last revision: January 12, 2024
Commit: [AppNodeWiseMeshPartitioner] Determine / append ghost nodes 8da02368
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