cons_flux_1d_unit Subroutine

private pure subroutine cons_flux_1d_unit(g, hf)

High-order freestream-consistent CONSERVATIVE-FLUX face values of a unit-spacing nodal line g(1..n): hf(1..n+1), where face iface lies between node iface-1 and node iface. The construction guarantees the telescoping identity

hf(i+1) - hf(i) = D[g](i)   (the matching high-order central derivative)

EXACTLY (to round-off) at every node, interior AND boundary. Because the nodal derivatives AND the transverse face metrics are BOTH built from this single operator, and central operators on the two computational axes commute discretely, the discrete metric identity Delta_xi(S_xi) + Delta_eta(S_eta)=0 holds to round-off on ANY map — the high-order freestream-consistent metric of Visbal-Gaitonde (2002) / Nonomura-Iizuka-Fujii (2010) (design spec §5.3).

Interior faces use the symmetric width-w conservative flux (w = cons_width): * w=6: [1,-8,37,37,-8,1]/60, whose undivided difference is the 6th-order central first derivative; * w=4: [-1,7,7,-1]/12 (4th-order central); * w=2: the classical [1,1]/2 (2nd-order central — the legacy operator). Near a boundary the symmetric stencil is closed by high-order polynomial extrapolation of the w nearest interior nodes into the w/2 ghost values it needs. Extrapolation keeps the operator a FIXED LINEAR stencil (so the cross-axis operators still commute, hence freestream is exact) while keeping the closure high order; for the smooth body-fitted maps of interest this boundary closure does not degrade the global convergence order.

Arguments