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Dirichlet (fixed value) boundary conditions

Supports: 1D and 2D (selected automatically based on domain)

1D

Sets the field value at the two boundaries:

where \( v_L \) is the value at the left boundary and \( v_R \) at the right.

2D

The same two values apply to all four edges:

• Left edge (x = 0): \( f_{i,0} = v_L \)
• Right edge (x = L): \( f_{i,-1} = v_R \)
• Bottom edge (y = 0): \( f_{0,j} = v_L \)
• Top edge (y = L): \( f_{-1,j} = v_R \)

value_left is used for the “min” boundaries (left, bottom); value_right for the “max” boundaries (right, top).

YAML

boundary:
  type: dirichlet
  value_left: 0.0
  value_right: 1.0