But more reasonable guess can speed up the convergence.
Boundary conditions
–
No-slip or slip-free on the wall, periodic, inlet (velocity
inlet, mass flow rate, constant pressure, etc.), outlet
(constant pressure, velocity convective, buffer zone,
zero-gradient), and non-reflecting (compressible flows,
such as acoustics), etc.

36
Grid generation
Grid generation
Grids can either be structured (hexahedral) or
unstructured (tetrahedral).
Depends upon type
of discretization scheme and application
–
Scheme
Finite differences:
structured
Finite volume or finite element:
structured or unstructured
–
Application
Thin boundary layers best resolved
with highly-stretched structured grids
Unstructured grids useful for complex
geometries
Unstructured grids permit automatic
adaptive refinement based on the
pressure gradient, or regions of
interest (FLUENT)

37
Grid Resolution
Grid Resolution

38
Grid generation and transformation
Grid generation and transformation
Grids designed to resolve important
flow features which are dependent
upon flow parameters (e.g., Re)
Commercial codes such as Gridgen,
Gambit
For research code, grid generated by
one of several methods (algebraic vs.
PDE based, conformal mapping)
For complex geometries, body-fitted
coordinate system will have to be
applied (next slide). Grid
transformation from the physical
domain to the computational domain
will be necessary
Sample grid established by
Gambit of FLUENT

39
Grid transformation
Grid transformation
y
x
o
o
Physical domain
Computational domain
x
x
f
f
f
f
f
x
x
x
y
y
f
f
f
f
f
y
y
y
Transformation between physical (x,y,z)
and computational (
) domains,
important for body-fitted grids. The partial
derivatives at these two domains have the
relationship (2D as an example)

40
Numerical parameters & flow
Numerical parameters & flow
solution
solution
Numerical parameters are used to control flow solution.
–
Under relaxation factor, tridiagonal or pentadiagonal solvers
–
CFD Labs using FlowLab
Monitor residuals (change of results between iterations)
Number of iterations for steady flow or number of time steps for unsteady flow
Flow solution
–
Solve the momentum, pressure Poisson equations and get flow field quantities, such as velocity, turbulence intensity,
pressure and
integral quantities (drag forces)

41
Numerical parameters & flow
Numerical parameters & flow
solution
solution
Typical time
history of
residuals
The closer the
flow field to the
converged
solution, the
smaller the speed
of the residuals
decreasing.
Solution converged, residuals do
not change after more iterations

42
Post-processing
Post-processing
Analysis, and visualization
–
Calculation of derived variables
Vorticity
Wall shear stress
–
Calculation of integral parameters:
forces, moments
–
Visualization (usually with commercial software)
Simple X-Y plots
Simple 2D contours
3D contour carpet plots
Vector plots and streamlines (streamlines are the lines
whose tangent direction is the same as the velocity vectors)
Animations (dozens of sample pictures in a series of time
were shown continuously)

43
Post-processing (Parallel Plates)
Post-processing (Parallel Plates)

44
Post-Processing (example)
Post-Processing (example)
Pressure contour and
velocity vectors .

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- Fall '19