torus_solver.surface_ops

torus_solver.surface_ops.contravariant_components_torus(surface, v_xyz)[source]

Return contravariant components (v^θ, v^φ) of a tangential vector field on the torus.

The torus parameterization has F=0 and metric coefficients E=a^2 and G=(R0+a cosθ)^2, so v · r_θ = E v^θ and v · r_φ = G v^φ.

Return type:

tuple[Array, Array]

Parameters:
torus_solver.surface_ops.surface_divergence_torus(surface, v_xyz)[source]

Surface divergence of a tangential vector field on the circular torus.

Return type:

Array

Parameters:
Using contravariant components (v^θ, v^φ):

div_s v = (1/sqrt(g)) [ ∂_θ (sqrt(g) v^θ) + ∂_φ (sqrt(g) v^φ) ].