Fig.1

Face-centered edge-normal method

Fig.2

Reconstruction of stencils with CWLSQ-V method

Fig.3

Reconstruction of stencils with CWLSQ-WA（n） method

Fig.4

Reconstruction of stencils with CWLSQ-GG method

Fig.5

Reconstruction of stencils （internal cell） with NFWLSQ method

Fig.6

Schematic diagram of NFWLSQ method of cell gradient reconstruction

Fig.7

Example of odd-even decoupling for NFWLSQ method

Fig.8

Schematic diagram of boundary constraint algorithm

Fig.9

Schematic diagram of three-dimensional local coordinate system

Fig.10

Typical grids for testing convergence

Fig.11

Convergence of Y-direction gradient L∞ error of different reconstruction method （internal cells）

Fig.12

Convergence of Y-direction gradient L2 error of different reconstruction method （boundary cells）

Fig.13

Computational grid and initial density contours of isentropoc vortex problem

Fig.14

Density error contours of isentropic vortex problem at t=2.0

Fig.15

Full field density error L2 for different methods

Fig.16

Mach number contours around cylinder

Fig.17

Entropy contours around cylinder

Table 1

Maximum entropy errors around circular cylinder

Fig.18

Total pressure recovery coefficient curves of wall boundary cells around an inviscid cylinder

Fig.19

Face-center normal velocity at downstream wall boundary of cylinder

Fig.20

Partial grids around NACA0012 airfoil

Fig.21

Entropy contours around NACA0012 airfoil trailing edge

Fig.22

Grid used for three-dimensional ellipsoid inviscid flow simulation

Fig.23

Entropy contours of Z=0 slice and elliposidal surface

Table 2

Elliposidal drag coefficient

Fig.24

Grids around cylindrical of subsonic viscous flow

Fig.25

Dimensionless pressure contours around cylindrical of subsonic viscous flow

Table 3

Separating vortex length ΔL and drag coefficient CD of subsonic viscous around a cylindrical

Fig.26

Convergence history of maximum density residual curves of different method （Mesh2）

Fig.27

Maximum density residual curves of different method （Mesh3）

Fig.28

Calculation area and boundary conditions of laminar flat-plate boundary layer flow

Fig.29

Grids of laminar flat-plate boundary layer

Fig.30

Velocity profiles of quadrilateral grid

Fig.31

Skin-friction factor along plate of quadrilateral grid

Fig.32

Maximum density residual curve for triangles grid of different methods

Fig.33

Velocity profiles of triangles grid

Fig.34

Skin-friction factor along plate of triangles grid