Answer Happy

7. The staggered-grid arrangement stores velocity and pressure at different locations. The u and v (the x and y components of velocity) are stored at the nodes indicated by arrows and the pressure p is stored at the circular nodes A-D (refer to the grid sketch). At an intermediate stage of calculation, the internal velocity values are found to be: Up = 12 , up = 15, vc = 10, vp = 7 The correction formulae derived from the momentum equation are: u' = 2(Pw - pė), v' = 2(p's - PM) - where, geographical notation W, E, S, N indicates the relative location of pressure nodes. Obtain the pressure correction equations by applying mass conservation to control volumes centered on pressure nodes. Solve for the pressure corrections and use them to generate a mass-consistent flow field i.e. velocity components at the interior nodes (up, up, Vc, Vp). The problem sketch along with the velocity values on the boundaries is shown below. The grid spacing is considered uniform and same in both the directions. (18 marks) f 10 10 C 20 . ivo Tvo CO ų B L to 15 10