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Boundary conditions hierarchy

Boundary conditions hierarchy

Boundary Conditions Hierarchy in Twin Fabrica

In Twin Fabrica, multiple boundary conditions can be applied to the same geometrical entity. Understanding how these conditions interact—and which take precedence—is essential to correctly modeling thermal behavior.

This section demonstrates the hierarchy and interaction rules of boundary conditions using a simple model that includes two convective conditions and one Neumann condition, with a final test involving a Dirichlet condition.

1. Overview of the Scenario

The model consists of two disk-shaped geometrical entities forming a simplified cable system. Three boundary conditions are used in various configurations:

  • convection_1 – a global convective condition
  • convection_2 – a local convective condition acting on Entity_1
  • neumann_1 – a localized heat flux condition on Entity_1
All boundary conditions are applied and tested in isolation and combination to observe their effects.

2. Initial Configuration – Convective Conditions Only

  • convection_1 is applied globally to all entities, modeling heat exchange with an ambient temperature (Tamb) and coefficient h.
  • convection_2 is applied only to Entity_1, using the same Tamb but a different coefficient h2.
  • neumann_1 is present but initially disabled (set to 0 W) to isolate the effect of the convective conditions.

3. Simulation Observations (Convective Only)

  • Entity_1 is influenced by both convection_1 and convection_2, increasing its total heat exchange.
  • Entity_2 is influenced only by convection_1.
  • As a result, Entity_2 exhibits a slightly higher temperature, due to lower overall cooling.

4. Enhanced Convective Cooling

  • The convective coefficient h2 in convection_2 is increased to 500 W/m²K.
  • This intensifies cooling on Entity_1, further lowering its temperature and increasing the contrast with Entity_2.

5. Replacing Convection with Neumann Condition

  • convection_2 is now disabled, and neumann_1 is activated with a heat input of 2000 W applied to Entity_1.
This directly replaces the additional convective cooling with localized heating.

6. Simulation Observations (Neumann + Global Convection)

  • Entity_1 becomes noticeably hotter than Entity_2, due to the new power input from neumann_1.
  • convection_1 continues to act globally, but is no longer sufficient to balance the local heating.

7. Return to Global Convection Only

  • neumann_1 is now disabled, leaving only convection_1 active across the entire model.
The simulation now shows a symmetrical temperature distribution, as expected in the absence of localized inputs.

8. Applying a Dirichlet Condition

  • A Dirichlet boundary condition is now configured on Entity_1, prescribing a fixed temperature.
  • All other conditions remain unchanged.
After rebuilding the Full-Order Model (FOM) and rerunning the simulation, the results show that Entity_1 holds exactly the imposed temperature.

9. Key Takeaway: Boundary Condition Precedence

This demonstration confirms the hierarchy of boundary conditions in Twin Fabrica:

Boundary Condition Precedence (from highest to lowest):

  1. Dirichlet condition – Always takes precedence and overrides any other type of condition on the same entity.
  2. Neumann condition – Applies a direct heat flux, unless a Dirichlet condition is present.
  3. Convective condition – Applies unless overridden by either Dirichlet or Neumann.

This hierarchy ensures that the solver prioritizes boundary conditions correctly and produces predictable, physically consistent results.