2-D prototype, round 2: symmetric compact schemes for Neumann / Robin / Dirichlet on the disc.
Gates (D = R = 1): Robin eigenvalue x J1(x) = Bi J0(x) -> mu = x^2 (Bi=0 Neumann j'11^2 is
the SECOND eigenvalue; Bi=inf is Dirichlet j01^2).
Schemes (all symmetric, <= 5-point rows):
P Papac-Gibou-Ratsch 2010: aperture FV, kappa mass, every kappa>0 cell, wall term k*A_w*u_P
RF aperture FV, kappa mass, wall flux A_w u_P / (d_centroid + 1/k) (round 1)
H* "aperture + link": unknowns = centre-fluid cells; slivers (kappa>0, centre in solid) merged
into their fluid-centred face neighbours (mass shared by aperture); fluid-fluid faces
aperture-weighted; each axis link P->S crossing the wall carries the Gibou distance theta
and a film over the wall area it represents, A_link = h |n_a|:
G_link = 1 / (theta/D + 1/(k |n_a|)) (per unit depth, flux = G (u_P - u_s))
H-k : mass = kappa_P + merged sliver shares
H-1 : mass = 1 (point values, Gibou)
Hf-1: same as H-1 but fluid-fluid faces fully open (pure Gibou + Robin links)
1.9.8