slayton58
commented
9 years ago Yes, it looks like 6.20 should have u_j on the left hand side, and maybe 6.21 should be changed a little for clarity:
1/2 u_i (x0) = -1/8\mu\pi \sum{J=1}^N tj \int{\Gamma} G_{ij}(x_0, x_J) d\Gamma_j + 1/8/\pi uj \int{\Gamma} T_{ijk}(x_0, x_J) \cdot n_k d\Gamma_j
On Jun 2, 2015, at 8:52 AM, Lorena A. Barba notifications@github.com wrote:
Stokes is a vector equation, so when you write u_i in Ch. 6, it represents the components of the u-vector: u_1, u_2, u_3 --- see equations 6.10 to 6.14, 6.16, 6.17. Then, in equation 6.19, there's some indicial notation magic and we have u_j on the left and u_i on the right multiplying with other tensors. Should equation 6.20 also have u_j on the left, then? (this is still a velocity component) On equation 6.21, j is used as the index to count panels. And my little head goes boom. Help!
— Reply to this email directly or view it on GitHub https://github.com/barbagroup/inexact-gmres/issues/7.
labarba
Stokes is a vector equation, so when you write u_i in Ch. 6, it represents the components of the u-vector: u_1, u_2, u_3 --- see equations 6.10 to 6.14, 6.16, 6.17. Then, in equation 6.19, there's some indicial notation magic and we have u_j on the left and u_i on the right multiplying with other tensors. Should equation 6.20 also have u_j on the left, then? (this is still a velocity component) On equation 6.21, j is used as the index to count panels. And my little head goes boom. Help!