High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils

Table 1

Specification of a fifth-order lattice-Boltzmann stencil: 𝑎_𝑠=1.148732248838539. The second column indicates the number of velocity vectors, obtained by permutating the vector components, sharing the given weight.

𝐜^⋆𝑖	𝑝	𝑤𝑖 (D2V49)
(0, 0)	1	2.1486215695621588×10^−1
(±1, 0)	4	1.0466324937773665×10^−1
(±1, ±1)	4	5.9279902836032117×10^−2
(±2, 0)	4	1.6329411241508002×10^−2
(±2, ±1)	8	6.6560728515645176×10^−3
(±2, ±2)	4	1.4236189699711052×10^−3
(±3, 0)	4	3.8641376938724455×10^−4
(±3, ±1)	8	4.4284732290059492×10^−4
(±3, ±3)	4	2.9169039140666429×10^−6
(±5, 0)	4	8.8685055032561952×10^−7
(±4, ±4)	4	2.2046291628739507×10^−7