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How to approach calculating a stream function given a velocity profile on a gridI have the velocity profiles for a 12x12 grid. So a 12x12 grid for the velocity in the x direction (u) and a 12x12 gride for velocity in the y direction(y) the stream function is defined as u=d(phi)/dy and v=d(phi)/dx. Where phi is the stream function.
This is a cavity flow: At the left, right, and bottom of the grid, the walls are stationary, therefore phi=0. To the right the change in phi (d(phi)) is the velocity in the y direction (v) times the change in distance going to the right (dx). Denoting each grid line in the x direction as i, In summary: d(phi) = dy * u ----> (phi)i+1 = (u)i*(dy)i+(phi)i Thoughts on my approach? |

[QUOTE=ComFlu;233904]I have the velocity profiles for a 12x12 grid. So a 12x12 grid for the velocity in the x direction (u) and a 12x12 gride for velocity in the y direction(y) the stream function is defined as u=d(phi)/dy and v=d(phi)/dx. Where phi is the stream function.
If u = d(phi)/dy then v = - d(phi)/dx. The minus sign is mandatory. [Or you can go with u = - d(phi)/dy and v = d(phi)/dx. If you carry the signs consistently throughout the derivations, either will work.] |

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