FLOW AROUND A CYLINDER - istiarto

– 4.51 –
��
�� �� �� NIT
u,v,w 10 �6 [m 4 /s 2 ] 10 �3 2
p 10 �5 [m 3 /s] 10 �2 20
k� 10 �6 [m 5 /s 3 ] 10 �3 5
� 10 �6 [m 5 /s 4 ] 10 �3 5
The calculation sequence is presented in the calculation diagram depicted in Fig. 4.14,
and is summarized as follows:
a) Initialize all dependent variable: ����� o �(u,v,w,p,k,� are given).
b) Define the geometrical properties, discretise the spatial domain.
c) Compute initial discharges, qcf, and eddy viscosity, �t.
d) Assign estimated pressures p � ,.
e) Construct coefficients of the discretized momentum equations.
f) Solve the momentum equations for u � , v � , and w � , consecutively.
g) Construct coefficients of the discretized pressure correction equation.
h) Solve the pressure-correction equation for p c and subsequently update the pressure, p,
and velocities at the cell centers, u, v, and w.
i) Compute the new discharge across cell faces, q cf .
j) Return to step ‗d‘ if the velocity components and pressure do not satisfy the
momentum and continuity equations.
k) Construct coefficients of the discretized k transport equation and solve for k; do the
same procedure to get �.
l) Compute the eddy viscosity, �t, from the new k and �
m) Update the water surface if the solution has converged, otherwise assign the new u, v,
w, p, k, and � as the new ‗old‘ values and return to step ‗d‘.
n) Stop the iteration if the steady-state solution has been reached, otherwise proceed to
the next time step, return to step ‗d‘.