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:
surface (TorusSurface)
v_xyz (Array)
- 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:
surface (TorusSurface)
v_xyz (Array)
- Using contravariant components (v^θ, v^φ):
div_s v = (1/sqrt(g)) [ ∂_θ (sqrt(g) v^θ) + ∂_φ (sqrt(g) v^φ) ].