[SOLVED] EG501V Computational Fluid Dynamics AY 2023/24 Tutorial 6 C/C

Tutorial EG501V Computational Fluid Dynamics (AY 2023/24)

Tutorial 6. Navier-Stokes, pressure correction – With solutions

Velocity, pressure, distance etc. are all dimensionless in this tutorial.

The discrete version of the pressure-correction equation reads (LN07, Eq. 7.8)

Consider the situation sketched in the figure which represents two-dimensional flow in a channel with a solid wall as the lower boundary, constant (and known) pressure at the left boundary, a symmetry condition at the upper boundary, and zero-gradient at the right boundary. In terms of the pressure correction π :∂ ∂ = π n 0 on all boundaries except for the left boundary which has π = 0. Further given the preliminary velocity values as in the figure, determine the matrix-vector system [A] = that needs to be solved in order to determine (which is the vector containing the 9 pressure correction values in the same order as numbered in the figure).

Further given: hx = 1, hy = 0.5, ρ/∆t = 1.