6.4 Experiment 4
The last study is to check the spatial error term. We take the time step At =
1/2 s and use Crank-Nicholson scheme p = 1/2. Four different graded meshes are
used in the domain Q2, where
Q2 = {(x, y,z)10 < z < 100 kni, 25 km < x, y < 25 kmn}
and the grid points are chosen according to Equation (6.2) and Equation (6.3)
along the z-axis:
Case 1: 30 uniform grid points in the x- and y-directions, and 100 grid
points in the z- direction (mesh size = 400 m for 0 < z < 20 km, and
exponentially increasing mesh for 20 < z < 100 km, from Az = 400 m near z
= 20 km to Az = 8043.61 m near z = 100 km).
Case 2: 60 uniform grid points in the x- and y-directions, and 200 grid
points in the z- direction (mesh size = 200 m for 0 < z < 20 km, and
exponentially increasing mesh for 20 < z < 100 km, from Az = 200 m near z
= 20 km to Az = 4652.41 m near z = 100 km).
Case 3: 120 uniform grid points in the x- and y-directions, and 400 grid
points in the z- direction (mesh size = 100 m for 0 < z < 20 km, and
exponentially increasing mesh for 20 < z < 100 km, from Az = 100 m near z
= 20 km to Az = 2629.65 m near z = 100 km).
Case 4: 240 uniform grid points in the x- and y-directions, and 800 grid
points in the z- direction (mesh size = 50 m for 0 < z < 20 km, and
exponentially increasing mesh for 20 < z < 100 km, from Az = 50 m near z
= 20 km to Az = 1462.03 m near z = 100 km).
Let "n, 02n, 4n,, and "8n denote the discrete potential evaluated along z-
axis at z = 10 km, where n, 2n, 4n, and 8n are the numbers of mesh intervals
along z-axis in case 1, 2, 3, and 4 respectively. We focus on z = 10 km since the