Adaptivity with moving grids

64 C. J. Budd, W. Huang and R. D. Russell
2
2
1.5
1.5
1
1
0.5
0.5
y
0
y
0
-0.5
-0.5
-1
-1
-1.5
-1.5
-2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
x
(a) M iso, (l, m) =(2, 1)
-2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
x
(b) M ani,2, (l, m) =(2, 1)
Figure 3.5. Example 3. Adaptive meshes of size N =81× 81
obtained using the variational method (2.40) (θ =0.1) for different
monitor functions based on isotropic and anisotropic interpolation
error estimates.
Z
1
X
1
Y
0.8
0.8
0.6
0.4
z
y
0.6
0.4
0.2
0
0.2
0.4
y
0.6
0.8
1
1
0.8
0.6
0.4
x
0.2
0
0
0.2
0
0 0.2 0.4 0.6 0.8 1
x
(a) Winslow’s type; (k, m) =(1, 1)
(b) Winslow’s type; (k, m) =(1, 1)
Figure 3.6. Example 4. An adaptive mesh of size N =65× 65 × 65
obtained using the variational method (2.40) (θ =0.1) for a monitor
function based on interpolation error. (a) Cut-away plot of the
mesh. (b) Plane projection of slice at K z = 32 of the mesh in (a).