Hydrodynamics Solver: Nitrogen and Pentane Filtration

Check out this post for a more detailed description!

Directory Structure

• doc/ - compact documentation and progress tracking.
• src/ - source code.
  • main - entry point.
  • physics - physical and EoS parameters.
  • cfd - hydrodynamics solver.
  • thermo - thermodynamics functions.
  • computational - computational methods.
  • dump - data dump + plot.
  • SimulationParameters - simulation parameters.
• test/ - for unit testing.
• aux/ - supplementary problems leading up to main project.

Initial and Boundary Conditions

Methods Used

1. Second order finite difference method for spatial discretization using a staggered grid.

2. Explicit predictor-corrector method according to the Heun scheme for time integration.

3. Newton-Raphson method for finding pressure and gas saturation.

Algorithm

1. We are given the densities $\rho_i = \rho_i(t)$.

2. Finding the pressure and gas saturation using the Newton-Raphson method from the condition of equality of the pressure of the gas and the liquid:

$$P = P_1 \left( \frac{\rho_1}{s} \right) = P_2 \left( \frac{\rho_2}{1 - s}\right)$$

3. Calculation of fluxes from Darcy's law.

4. Calculation of the densities $\rho_i(t + \Delta t)$ based on the known fluxes.

5. Renaming $\rho_i = \rho_i(t + \Delta t)$ and moving on to the next time step.

Results

How to Run

TODO: PkgTemplates.jl

In normal mode:

julia src/main.jl

In debug mode:

JULIA_DEBUG=Main julia src/main.jl