# Test Case for Resolved Interface Drag

## Description

This test is designed for testing against the analytical solution for a
stratified laminar flow. The fluid on the top ($`\mu_2`$) and the fluid at the
bottom ($`\mu_1`$) are both driven by a constant volume force with same
strength but opposite direction. Bottom and top wall allow slip.

Assume that the interface between both fluids is located at $`y=0`$ and that
there acts a volume force according to:

```math
q =
\left\{\begin{array}{lr}
        - K & \text{for} &  0 < y \le h \\
        + K & \text{for} & -h \le y < 0
\end{array}\right\}
```

The analytical solution for laminar fully developed flow is:

```math
u - U_\mathrm{I} =
\left\{\begin{array}{lr}
        + \frac{K}{\mu_2} \left( \frac{1}{2} y^2 - hy \right) & \text{for} &
            0 \le y \le h \\
        - \frac{K}{\mu_1} \left( \frac{1}{2} y^2 + hy \right) & \text{for} &
            -h \le y \le 0
\end{array}\right\}
```

The interface velocity $`U_\mathrm{I}`$ is arbitrary and mainly results from the
given initial condition.

This particular version of the case is set up to use the Coste drag considering
the estimated interfacial shear stress for an under-resolved interface of finite
thickness. Hence, an interfacial slip velocity is allowed to improve the overall
momentum transfer across the interface delivering more precise velocity profile
prediction compared to the resolving interfacial drag model approach.

## Technical Information

- horizontally cyclic flow
- top and bottom: slip walls
- volume fraction is fixed in time
- domain consists of a single vertical row of cells
- no gravitational acceleration

## Pre-Processing

Volume fraction is initialised with a third order polynomial distribution by
means of a coded functionObject *generateAlphas*.

## Post-Processing

GraphCell is used to record cell values. The analytical solution is plotted as a
reference.

## Keywords

1.5D, cyclic, multiphase, steady-state, isothermal, incompressible, interface,
analytical-solution
