Heat and Mass Transfer with Phase Change

In this repository you will find a list of simulation regarding the effect of phase change on heat and mass transfer. All of the programs use the Finite Element Method, which is implmented on C++ with the library MFEM.

In each of the simulations, the domain is a cylinder, sometimes hollow, with an axial symmetry. Inside the domain, it is assumed that the material is water, which can be liquid and solid.

Running the programs

1. Copy the hidden file .template_local_config.txt with the name local_config.mk
2. Add the MFEM instalation directory.
3. If you want to move the graphs to other folder after running a program, change the NULL option of the SHARE_DIR variable to the folder directory.
4. If you want to chage some quantity on a simulation, in each folder the file settings/parameters.txt has all the main parameters of the simulation.
5. To run a simulation, you only have to write make.

List of programs

• Time_Independent
  • 3D: Benchmark Poisson equation problem with convergence analysis on a 3D hollow cylinder.
  • 2D: Benchmark Poisson equation problem with convergence analysis on a 2D square which simulates a hollow cylinder on cylindrical coordinates (the rest of the simulations assume this domain representation).
• Time_Dependent
  • onephase: Benchmark time dependent heat equation with convergence analysis, in which only one phase is present.
  • twophase: Simulation with initial conditions set on different phases.
  • twophase_exact: Stefan problem simulation with comparison according to the exact Stefan solution.
• Flow
  • vorticity: Quasi-static flow problem with a stream function-vorticity formulation and a frozen region.
  • vorticity_barrier: Quasi-static flow problem with a stream function-vorticity formulation and an obstacle.
  • vorticity_exact: Benchmark quasi-static flow problem with a stream function-vorticity formulation, including a convergence analysis.
• Coupled
  • heat_flow: Heat diffusion problem with convection effects, where the flow is quasi-static and approched by a stream function-vorticity formulation.
  • double_diffusion: Heat and salinity diffusion problem, where both variables are weakly coplued.
  • diffusion_flow: Heat and salinity diffusion problem, where both variables are weakly coplued, including convection effects with a quasi-static flow and a stream function-vorticity approach.
• Brinicle
  • Simulation from diffusion_flow applied to form a brinicle, which is an ice channel formed on the artic sea because of icy brine fluxes that enter the ocean from the top layer of ice.