Transport of water–air mixture

This test case, realised with the Discrete Equation Method and the HLLC Riemann solver, is important since it validates the capacity of the numerical method to treat advection of a mixture between fluids without creating spurious oscillations on pressure or velocity profiles. The equation of state used is stiffened gas with \(\gamma = 1.4\) and \(P_{\infty} = 0\) for air and \(\gamma = 4.4\) and \(P_{\infty} = 6 \times 10^{8}\) for water. Input files for this test are available in ./libTests/referenceTestCases/NEqDEM/1D/transport/waterAirAlphaDiff/. The corresponding uncommented line in ECOGEN.xml is:

<testCase>libTests/referenceTestCases/NEqDEM/1D/transport/waterAirAlphaDiff/</testCase>

\[ \begin{array}{|c|c|c|c|c|} \hline & \text{High pressure} & \text{High pressure} & \text{Low pressure} & \text{Low pressure} \\ \hline \text{Phase} & \text{Water} & \text{Air} & \text{Water} & \text{Air} \\ \hline \rho \, [\text{kg/m}^3] & 1000 & 100 & 100 & 1 \\ \hline u \, [\text{m/s}] & 20 & 20 & 20 & 20 \\ \hline P \, [\text{Pa}] & 10^{5} & 10^{5} & 10^{5} & 10^{5} \\ \hline \end{array} \] Initial conditions for 1D advection of water-air mixture.

The initial characteristics of the run are:

\begin{array}{|l|l|} \hline \textbf{Characteristic} & \textbf{Value} \\ \hline \text{dimension} & 1 \text{ m} \\ \text{mesh size} & 400 \\ \text{interface position} & 0.4 \text{ m} \\ \text{boundary conditions} & \text{non-reflecting} \\ \text{final solution time} & 2 \times 10^{-2} \ \mathrm{s} \\ \text{solution printing frequency} & 1 \times 10^{-3} \ \mathrm{s} \\ \text{precision} & \text{1st order} \\ \hline \end{array}