1. Arvind Deshpande

2. 1. Take the input from the user :Initial
temp(Tinitial), Boundary condition information,
material properties density, thermal
conductivity, specific heat, length, height, no.
of interior control volumes control volumes in
x-direction and no. of control volumes in y-
direction and time step (based on stability
criterion).
2. Calculate x and y coordinates for all points.
3. Calculate aw, ae, an, as and ap for all cv’s.
Formula changes for cv’s close to boundary.
4. Implement all boundary conditions.

3. 5. Set Told and Toldt= Tinitial for all cv’s and Tnew
= 0 for all cv’s.
6. Increase time by time step and calculate
Tnew at all cv’s using Gauss-Seidal point by
point or line by line TDMA method.
7. Check for convergence for iterations within
time step. Residual = Tnew – Told (max
residual /average residual/rms residual <ε)
8. If converged, goto step 9 otherwise assign
Told = Tnew and go to step 6.

4. 9. Check for “steady state” Residual = Tnew –
Toldt (max residual /average residual/rms
residual <ε)
10. If converged, stop otherwise assign Toldt =
Tnew and go to step 6.

5. 1. Take the input from the user :Inlet temp of
flow, Boundary condition information, material
properties density, thermal conductivity,
specific heat, length, height, no. of interior
control volumes control volumes in x-direction
and no. of control volumes in y-direction.
2. Calculate x and y coordinates for all points.
3. Calculate velocity u and v using given formula.
4. Calculate Dw, De, Dn, and Ds for all cv’s. Formula
changes for cv’s close to boundary.

6. 5. Based on CDS/UDS/Hybrid calculate aw, ae,
an, as ap for all cv’s. Formula changes for
cv’s close to boundary.
6. Implement all boundary conditions.
7. Set Told and Tnew = 0 for all cv’s.
8. Calculate Tnew at all cv’s using Gauss-Seidal
point by point or line by line TDMA method.
9. Check for convergence. Residual = Tnew –
Told (max residual /average residual/rms
residual <ε)

7. 9. If converged, goto step 10 otherwise assign
Told = Tnew and go to step 6.
10. For each axial location, calculate bulk mean
temp, heat transfer coefficient and Nusselt
no.

8. Solution algorithm – Lid driven cavity (SIMPLE)

9. 1. Take the input from the user :Lid velocity,
material properties density, dynamic viscosity,
length, height, no. of interior control volumes
control volumes in x-direction (j) and no. of
control volumes in y-direction (i), under
relaxation factor for pressure and velocity. (You
can use recommended under relaxation factors)
2. Calculate x and y coordinates for all points.
3. Implement all boundary conditions.
4. Set uold =unew = vold =vnew =Pold =Pnew = 0 for all
interior cv’s.

11. 5. Calculate Dw, De, Dn, and Ds for all cv’s.
6. Calculate Fw, Fe, Fn, and Fs for all cv’s. You will
have to use interpolation (average) for velocity.
7. Based on CDS/UDS/Hybrid calculate aw, ae, an, as
for all cv’s. Formula changes for cv’s near top and
bottom boundary.
8. Calculate ap , source term based on pressure
gradient and d1 values for all cv’s.
9. Solve X-momentum equation (modified with
under-relaxation factors) to get new values of u
using Gauss-Seidal method.

13. 10. Calculate Dw, De, Dn, and Ds for all cv’s.
11. Calculate Fw, Fe, Fn, and Fs for all cv’s. You will
have to use interpolation (average) for velocity.
12. Based on CDS/UDS/Hybrid, calculate aw, ae, an, as
for all cv’s. Formula changes for cv’s near left and
right boundary.
13. Calculate ap , source term based on pressure
gradient and d2 values for all cv’s.
14. Solve Y-momentum equation (modified with
under-relaxation factors) to get new values of u
using Gauss-Seidal method.

15. 15. Calculate aw, ae, an, as for all cv’s. Formula
changes for cv’s near boundary.
(Corresponding coefficient will be zero)
16. Calculate ap , source term (mass source)
for all cv’s.
17. If mass source < ε , solve pressure
correction to get new values of P’ using
Gauss-Seidal method.
18. Pressure correction at boundary points
can be set based on zero gradient.

16. 19. Correct pressure using under relaxation
factor. Correct velocity without under
relaxation.
20. If mass source < ε, go to next step. Otherwise go
to step 5 with uold =unew , vold =vnew , Pold =Pnew
21. Calculate u-velocity profile at vertical centreline
and v-velocity profile at horizontal centreline and
compare with bench mark results.
(GHIA et al. (1982) JOURNAL OF
COMPUTATIONAL PHYSICS VOL. 48,
pp.387-411)

18. Convergence criteria No. of iterations
10-5 736
10-6 1531
10-7 3262
10-8 5924

21. No. of Control volumes No. of iterations
10 X 10 202
20 X 20 710
40 X 40 2243
80 X 80 5924