Multi-physics implementation

[Ray Mclaren]

Hi,

I have a question regrading multi-physics problem implementation.

I am developing a program that will solve the steady-state thermal conduction (laplace) first and then the allen-Cahn equation.

both of the problems are solved on the same mesh, however due to the nature of my specific implementation they solved separately. To solve the allen-Cahn equation, I need to evaluate temperature dependent functions at each node in the domain.

Hence, they only share the same triangulation, but everything else is separate.

My question is, how to use the solution vector from the thermal conduction (the temperature) in the assembly of the allen-cahn equation ?

 how to access the temperature at these nodes and make sure that they are synchronized ? 

thank you

[simon...@gmail.com]

Hi,

I would do it like this:

  // Setup two DoFHandlers, one for the heat and one for Allen-Cahn
  DoFHandler<dim> heat_dof_handler(triangulation);
  DoFHandler<dim> allen_cahn_dof_handler(triangulation);

   // Solve for this first
  Vector<double> heat_solution;

  // Lots of things in between here...

  // When assembling for allen_cahn, create two FEValues objects.
  FEValues<dim> fe_values(allen_cahn_element, quadrature, update_flags);
  FEValues<dim> heat_fe_values(heat_element, quadrature, update_values);

  for (auto cell : allen_cahn_dof_handler.active_cell_iterators())
    {
      // Cast to an iterator on the heat_dof_handler
      typename DoFHandler<dim>::active_cell_iterator heat_cell(
        &triangulation, cell->level(), cell->index(), &heat_dof_handler);

      // Call reinit with the corresponding cells.
      fe_values.reinit(cell);
      heat_fe_values.reinit(heat_cell);

      // Get the heat values at the quadrature points using heat_fe_values
      std::vector<double> heat_values(heat_element.dofs_per_cell);
      heat_fe_values.get_function_values(heat_solution, heat_values);

      // Assemble the system using fe_values here ...
    }

Best,

Simon

[Ray Mclaren]

Mr. Simon

thank you for your response, It was exactly what I was looking for. 

[Jean-Paul Pelteret]

Hi Ray,

I’m happy to see that Simon has already given a great explanation as to how to solve your problem. It’s probably more on point than the code that mentioned that I would direct you towards. So it really was worthwhile asking the question again here :-)

Best,

Jean-Paul

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[Ray Mclaren]

Mr. Pelteret 

Sir, thank you for your guidance. 

I am new to using dealii and I am very thankful for your support

Thanks