Hello everyone.
So, today we will study the application of
CFD.
So, it is a introductory lecture.
CFD is the short form of Computational Fluid
Dynamics.
So, fluid dynamics you know that when we study
the fluid in motion then that is known as
fluid dynamics.
So, fluid dynamics is the science of fluid
motion, OK and CFD is the, this fluid dynamics
when we study numerically then that is your
CFD, Computational Fluid Dynamics, Computational
Fluid Dynamics.
Fluid flow is commonly studied in one of the
three ways, Experimental fluid dynamics, theoretical
fluid dynamics and computational Fluid Dynamics.
So, first one is experimental fluid dynamics,
so you can study the fluid dynamics doing
some experiments, so you can measure the temperature
with thermocouple or the velocity with pitot
tube and you can study what is the velocity
profile or the temperature profile using experimental
techniques.
Other way is that theoretical fluid mechanics
or fluid dynamics, you have the governing
partial differential equations, which represent
the fluid flow, heat transfer or other multi
physics problems.
So, when you write the partial differential
equations, we with some assumptions you can
write it to ordinary differential equations
and with the boundary conditions if you can
solve those equations, then you can have the
exact solution.
So, theoretical also you can study the fluid
dynamics, but you can study theoretically
under certain assumptions, because you have
to bring down this partial differential equation
to ordinary differential equation.
Like if you are studying the fully developed
fluid flow problem, then fluid fully developed
means there is no variation of velocity in
axial direction.
So, it essentially boils down to one dimensional
problem.
And with boundary conditions you can solve
and get the velocity profile theoretically.
The other way is to study this fluid dynamics
numerically.
So, you have the partial differential equations
using these computational fluid dynamics techniques,
you can solve the partial differential equation
and get the solution using computational fluid
dynamics.
So, computational fluid dynamics is the science
of predicting fluid flow, heat transfer, mass
transfer, chemical reactions and related transport
phenomena by solving the mathematical equations
which govern these processes using numerical
approach.
So, you can see that CFD is the calculation
of properties of a flowing fluid.
So, it is not only limited to fluid dynamics
but you can extend it to heat transfer, you
can mass transfer, then some other multi physics
problems, electro hydrodynamics flow or magneto
hydrodynamics flows or with chemical reaction
and many more.
CFD provides a qualitative and sometimes even
quantitative predication of fluid flow by
means of three ways, first one is mathematical
modelling, then numerical methods, then software
tools.
So, if you want to solve some problem, then
first you find or you write the partial differential
equations which govern the flow, so that is
your mathematical modelling, then you can
choose suitable numerical methods, like discretization
techniques and some solution techniques you
can choose.
Then you can use some software tools like
you can solve using some solvers those discretize
equations OK and get some solutions in terms
of data, so only numbers will be there as
output.
So, to visualize this data you can use some
post-processor and in the pre-processor you
need to give required boundary conditions
and initial conditions if required.
So, in post processing tools you will be able
to visualize those data and you can see the
velocity profile or temperature profile or
some contours using some post-processing tool.
So, we will now see the history of this CFD.
So, you can see that earlier CFD work started
in 1910.
And Richardson used human computers to solve
Laplace equation using finite difference method
and he solved flow over cylinder OK only for
the potential flow.
For inviscid flow he solved using finite difference
method.
So, in 1910 using human computer.
Then Courant and his research groups like
students, Friedrich and Lewy they solved the
hyperbolic equations in 1928.
Von Neumann in 1950 proposed the stability
criteria for parabolic problems, which is
known as Von Neumann stability analysis and
in this course we will study also this stability
analysis, Von Neumann stability analysis.
Harlow and Fromm computed unsteady vortex
street using digital computer in 1963.
And later Harlow and Welch published a scientific
American article which ignited interest in
modern CFD and the idea of computer experiments.
So, they solved first time the free surface
flow, which is a two component fluid flow
problems in 1965 using digital computer.
Professor Brian Spalding is known as the founding
father of CFD.
So, he and his research group developed this
boundary layer codes which is known as GENMIX
and in they developed these codes in the years
1960 to 1970s and 1972, they actually those
code they put as a software as known as GENMIX.
And Patankar is student of Professor Spalding
and they, their solution techniques for incompressible
flows is published through the 1960s and they
first time proposed the simple family of algorithms,
which we will study in this course for solving
the full Navier-Stokes equations.
Jameson computed Euler flow over complete
aircraft, so this is for compressible flows
Euler equation they solved and they published
almost 14 papers in 1981 on this using the
Euler flow solver.
Later this there was a problem because in
the structured mesh it is very difficult to
generate for a complicated geometry, so the
unstructured grid you can easily fit in a
complex geometry.
So, unstructured mesh methods developed in
1990s used for first used for aerodynamic
calculation in NASA.
So, later professor Murthy and her group developed
this unstructured grid solver for ANSYS Fluent.
And she and her co-workers developed different
modules in fluent.
And you can see the publications during the
development and now this Fluent is known as
ANSYS Fluent and most of you I think you use
this commercial structured ANSYS Fluent for
solving any problem numerically.
Now, who are interested in CFD?
So, practical problems may include multi-physics
like energy flow, chemical reaction, phase
change et cetera.
And that domain or computational domain mostly
these are three dimensional and very complicated.
So, it is relevant and so it is easier to
use the numerical technique to solve the governing
equations.
So, relevant industries include automotive,
chemical processing, aerospace, HVAC (heating
ventilation and AV conditioner); even nowadays
in biomedical applications we use CFD.
So, the results of CFD analysis is relevant
engineering data used in conceptual studies
of new designs, detailed product development,
troubleshooting and redesign.
CFD enables scientist and engineers to perform
numerical experiments in a virtual laboratory.
So, you can see this is a solution for flow
over a circular cylinder, you have a circular
cylinder and you have a fluid flow over it,
so if you do the real experiment OK the you
can see the visualization.
Now, if you do the CFD simulations, you will
get this type of simulation results.
So, you can see that you are doing actually
numerical experiments in a virtual flow laboratory.
CFD gives an insight into flow pattern that
are difficult, expensive or impossible to
study using traditional experimental techniques.
In experiment, it is very difficult to get
the velocity profile or temperature profile
at desired or different locations.
But, when you use this CFD technique, you
discretise these governing equations at a
discrete points.
So, you can get easily any value, velocity,
temperature or species at those discrete points.
So, it is easy to visualize the results in
terms of velocity contours or velocity vectors
or temperature profile.
CFD does not replace the measurements completely,
but the amount of experimentation and the
overall cost can be significantly reduced.
The doing experiment is costly, because you
need to fabricate the setup and also you need
different instrument to measure velocity,
temperature; so it is very costly.
So easily you can use this numerical techniques
to solve those partial differential equations
for a particular problem and get the solutions.
And equipment and personnel difficult to transport
and CFD software is portable, easy to use
and modify.
So, we can see that real experiments are expensive
whereas CFD simulations are cheaper; real
experiments are slow, CFD simulations are
faster; real experiment is sequential, CFD
simulations are parallel; real experiments
are single purpose, CFD simulation are multiple
purpose.
What does it mean?
That, when you are doing some experiment,
so you have made the setup, so you are doing
the experiment in the laboratory.
So, at a time you can do only single experiments
and obviously doing the experiment, fabricating
the setup it is very expensive.
Whereas if you develop a numerical solver
for solving that problems, fluid flow or heat
transfer problems, then once the code is ready
you can solve the problem for different conditions
parallely OK so, that means you can run that
solver in different computers for different
parameters.
So, parallelly you can run and obviously you
can see that it is very portable because you
can take the solver with you to somewhere
else, but it is very difficult to shift the
experimental setup from one location to other.
The results of CFD simulations are not always
100 percent reliable.
The input data may involve too much guessing
or imprecision.
The mathematical model of the problem at hand
may be inadequate.
The reliability of the CFD simulations is
greater for laminar flows than for turbulent
ones.
For single-phase flows than for multi-phase
flows and chemically inert system than for
reactive system.
When we solve these equations, we have some
assumptions, so obviously, when it becomes
more multi-physics then you have lesser reliability.
CFD is a highly interdisciplinary research
area, which lies at the interface of physics,
applied mathematics and computer science.
Now, let us see few examples or applications
of CFD applications, sorry, applications of
CFD.
So, first, we see in the Aerospace.
So, we can see that when you are actually
designing this aeroplane, obviously you can
solve the governing equations and you can
design such a way that you can have the minimum
drag while flying.
So, obviously, in designing the exterior even
for interior design also, you need the safe
dissimulations for the passenger comfort,
to design the combustor then pumps, missile
systems.
So, you can use this CFD to design these external
aerodynamics, propulsion, missile systems
and pumps.
CFD application in automobile, so obviously,
here also you can have the you can use CFD
for exterior design to reduce the drag, even
for the interior design you can use CFD so
that the air form the air conditioning reaches
to all the passengers to fill the comfort.
So, for interior design you can use the CFD,
even in the combustion chamber OK you can
use the CFD techniques and also for engine
cooling and external aerodynamics you can
use the CFD application in automobile.
So, you can see some in this animations one
car is there and you can see how the flow
physics looks behind this car.
So, it is very complex you can see, so it
is a numerical simulation.
So, some CFD application in process engineering
OK so, you can use it for reactor design,
heat exchanger, so here fluid flow and heat
transfer you can solve; mixtures, boiler pumps,
compressor and diffuser design you can use
this CFD.
This is some fan is moving and you can see
how the flow looks like.
CFD also you can apply in heating, ventilation
and air conditioning.
So, when you are designing some room for comfort
stay, you can use the CFD technique.
So, air flow around building, burner design,
environmental control system, heating system
design, room flow distributions, all this
you can use, to solve this problems you can
use CFD.
CFD is also having applications in electronics
cooling, so you can see that when you use
any computer or laptop you have the processor
and if processor is having high temperature,
so earlier days in your desktop you will find
a fan mounted on the processor and it is cooling.
So, these kind of things you can actually
solve using CFD, you can see this picture
where you can see the temperature distribution.
So, this is the fan and here you have the
processor with fin mounted on it, so the cooling
is taking place due to the forced convection,
here you can see it is the application in
heat pipe OK, so you can do the CFD analysis
for component level flow and cooling, electronic
chip cooling, magnetic storage devices, telecommunication
equipment.
So, some piezo electric device you can see
how the fluid flow is taking place, vortex
are generated.
You can also use CFD in sports, so you can
see when the ball is moving how the flow physics
looks behind the ball you can see from here
or if you are cycling then how the flow physics
behind you, you can solve using the CFD technique,
even for car racing and swimming you can use
CFD techniques.
Now, there are many applications in biomedical,
so blood flows through arteries, so we can
have the deformable arteries as well using
different advance technique you can simulate
this problems.
Heart pumps where you have a moving boundary
problems and for tumours you can have the
solution of the heat generation inside the
tumour and that you can model using CFD.
You can see this is the blood flow inside
the heart, so one-simulation results.
So, there are many applications of CFD in
many different industrial in industry and
you can see in that power generations, power
pants you can have the application of CFD;
in hydraulics, so hydraulic turbine all those
things you can model using CFD; oil and gas
industries, in marine industries, so there
are many applications OK in different kind
of industries.
So, the governing equations you can write;
with certain assumptions you can apply this
governing equation to some problem.
So, asssumptions may be like incompressible
flow, unsteady flow, laminar flow, Newtonian
fluids, single phase, constant properties.
So, for this you can write the governing equations.
So, obviously, all the equations you can have
the conservation laws, conservation of mass
where continuity equation you can write, conservation
of momentum where Navier-Stokes equation you
will write; conservation of energy, energy
equation; conservation of species, diffusion
equation.
So, you can see that this is your continuity
equation in general but if it is incompressible
flow, obviously it will be diversions of v
will be 0.
Then, you have general transport equations;
for any species you can write this equation,
especially for x momentum equation if you
write this equation then it is the temporal
term, this is your convective term and this
is your viscous term, this is the pressure
gradient term and if you have any source term
that you can write, energy equations in terms
of enthalpy if you write, then this is the
energy equation where k is the thermal conductivity.
Species transport equation in terms mass fraction,
Yi is the mass fraction, so that you can write,
so you can see you can see all these equations
you can write in a general transport equation
for a general variable, phi where S may be
different or the diffusion coefficient gamma
will be different.
So, when you have the governing equation you
need to use some discretization techniques,
so mainly in CFD we use three different techniques,
one is finite difference method, then finite
volume method and finite element method.
In this course, we will study only finite
difference method and finite volume method.
Finite difference method, generally we use
Taylor series expansion and find the approximation
of any derivative, first or second derivative
and we discretize the governing equations
and write the final algebraic equations.
When we use finite volume method then we integrate
the governing equation over a control volume
and write the discretize equation.
But, in finite element method we integrate
the governing equation with some waiting function
in a particular element and we write the discretise
equations.
So, obviously, in this course we will study
only finite difference method and finite volume
method.
To solve these governing equations you need
to discretise this domain into grid.
At those discrete point, you need to solve
the discretised algebraic equations.
So, now grid can be classified into two; structured
grid and unstructured grid.
So, as I told before that structured grid
are easy to generate in a simple geometry,
but if we have a complex geometry then it
is very difficult to generate structure mesh,
so you need to use, divide the domain into
blocks, and in the block you need to generate
the mesh.
But, unstructured grid is it is very easy
to fit into a complex geometry.
So, structured grid can be further classified
as regular grid, block structured grid and
curvilinear grid.
So, in the regular grid, regular structured
grid you can see these are actually orthogonal
in the coordinate system.
So, if it is we use Cartesian grid then these
grids are orthogonal to each other, it can
be uniform spacing or non-uniform spacing;
you can see here we have used non-uniform
spacing.
Cylindrical grid, so in cylindrical coordinate
system these are orthogonal to each other.
And in spherical grid, in spherical coordinated
the grids are orthogonal to each other.
So, these are regular structured grid.
Then block structured grid.
So, you have a complex geometry, then you
can divide the domain into zones and generate
the mesh and at the interface you keep the
continuityOK , make the continuity.
So, we can see it is some cylinder is there
in this here, so it is cylinder is there.
So this is divided into 1, 2, 3, 4, 5, 6,
7, 8, 8 subdomains and each domain the grids
are generated.
And it is a continuity is maintained at the
interface.
So, this is one representation of the grid
for a flow over circular cylinder.
So, these are known as block structured grid
because you are dividing the domain into blocks
and in each block, you are generating the
mesh.
Then curvilinear grid.
So, curvilinear grid are known as body fitted
grid, so you can see that the grids are following
the body, surface of the body.
So, here you can see if it is this is the
body the grids this is the grid so it is following
the body.
So, these are curvilinear structured grid,
so obviously, these girds are not orthogonal
you can see.
So, these are non-orthogonal grids.
And for different geometry you can see that
how the curvilinear grids are generated.
In curvilinear grids, as I told that, grids
will follow the boundary.
In unstructured grid, so we can have regular
grid and hybrid grid.
In regular grid, you can have same type of
cells OK, like hexahedral, tetrahedral, prism
or pyramid in 3D and triangular cell or quadrilaterals
in 2D.
And hybrid grids are grids where you can have
more than one type of cells; if you have hexahedral
cells and tetrahedral cells are mixed then
obviously you can have hybrid grid.
So, you can see here, so you can see that
in this case this first figure, you can see
the grids are fine near to the boundary to
capture the gradient more correctly or more
accurately.
So, local refinement you can do using unstructured
grid.
But, in structured grid, it is very difficult
to do local refinement because to maintain
the continuity this will be extended in other
directions.
So, in unstructured grid that’s why it is
very easy to use the local refinement.
And you can see you can use hybrid grid, hybrid
grid mean more than one type of cells if you
use.
In this case, you can see near to the boundary
you have quadrilateral cells and away from
the boundary, you have triangular cells.
So, that means near to the boundary you have
almost structure and orthogonal mesh so that
you can capture the gradient correctly OK
and away from the surface where you do not
have much gradient you can use triangular
cell, so this is kind of hybrid cell.
So, in 3D, you can have hexahedron type cells
or tetrahedron or pyramid or prism.
Nowadays, in commercial softwares they use
any type of poly hydra, but Ansys Fluent earlier
they used use only these four types of cells
for the three dimensional domain.
And for surface grid, triangular or quadrilateral
mesh are used.
So, you can see there are some advantages
and disadvantages of this structured and unstructured
grid.
So, you can see the structured grid, what
are the advantages, efficiency in CPU time
and computer memory OK, because in structured
grid you can easily find the neighbours, because
you have the indices I, J, K and I plus 1,
I minus 1, or J plus 1, or J minus 1, will
give you the neighbours.
So, less storage memory is required and it
is good environment for multigrid technique.
Whereas, in unstructured grid, advantages
are flexible for very complex geometry region
and it permits automatic adaptive refinement
based on regions of interest, so at the particular
region if you need very fine mesh then you
can use actually unstructured grid.
The disadvantages of the structured grid is
that lack of total flexibility for very complex
regions because you cannot do local refinement
and it cannot be distorted to increase resolution
in a localised region.
The unstructured grid disadvantages are there,
that requires more memory as compared to structured
grid to store the connectivity.
So, in unstructured grid you cannot find the
neighbours with the indices I plus1, I minus
1, because there is no structured way these
grids are oriented.
So, in pre-processing stage, you need to find
the neighbours or connectivity so that you
can use it later while calculating the fluxes.
So, obviously, you need more memory requirement
to store this connectivity and the neighbours’
informations.
And this another disadvantage for unstructured
grid is not necessarily amenable to the implementation
of multigrid.
So, now we will talk about the grid terminology.
So, when you discretise the domain for generally,
for finite difference method we solve the
equations, discretised algebraic equation
is solved at this grid node OK, which are
known as vertex.
But, in case of finite volume method we integrate
over this cell, so the value is stored at
the cell centre OK or cell centroid and this
is the cell and these are known as faces OK,
so in faces in two dimension it is line, but
it is three dimensional it will be a surface.
So, you can have node based finite volume
scheme where phi the variable stored at vertex,
or cell based finite volume method where the
variable stored at the cell centroid.
Based on the variable storage you can have
two different types of grid arrangement, one
is staggered grid and another is co-located
grid, we will learn more detail when we will
study the finite volume method, but here just
I will just introduces that, when all the
variables you store at the cell centre or
at the same node then it is known as co-located
grid.
So, you can see the velocities, pressure and
any species let us say temperature or any
species you can store at the cell centre at
the same point then this is known as co-located
grid.
But, you can see that it is very easy to have
that data structure, because all the variables
are stored at the cell centre, but it is having
some disadvantages, so that we will learn
later, that is known as velocity pressure
decoupling.
So, if you use co-located grid, it may be
possible that your velocity and pressure are
not talking each other because your velocity
there will be due to the pressure difference
there will be velocity, right.
So, if there is no pressure difference then
obviously there will be no velocity, so this
pressure and velocity if it is decoupled then
there will be problem, so that is known as
pressure velocity decoupling.
And when you have this checker boarding kind
of distribution of velocity or pressure then
you will get this type of problem in co-located
grid.
So, that we will discuss in detail later.
And in staggered grid to avoid this problem,
velocity pressure decoupling problem, we use
staggered grid, where we store the variables
at different places.
So, we solve the pressure and the scalars
like temperature or species at the cell centre
and the phase centre in staggered way we will
solve the velocities.
So, we can see in this figure, so if this
is the figure where we are solving at the
cell centre only the pressure and any scalar
like temperature or species, whereas we solve
the velocities at the at this cell.
So, this is velocity, U velocity and at this
cell we solve the V velocity.
So, you can see that U and V are solved at
staggered way and pressure and any scalar
are solved at the cell centre of the main
control volume.
So, this is the main control volume for pressure
and scaler but this is the control volume
for U velocity and this is the control volume
for V velocity.
So, in staggered grid, actually you can avoid
this pressure velocity decoupling, but you
can see that storage requirements are different.
Because as and U and V are solved at different
places, so you need to write the code carefully
so that you can take care about the data structure.
So, you can see that in co-located arrangements
store all the variables at the same set of
grid points and to use the same control volume
for all the variables.
Advantage, obviously, it is easy to code,
because all the variables are stored at the
same point.
Disadvantage is, pressure velocity decoupling.
And in staggered arrangement, not all variables
share the same grid, so advantage is strong
coupling between pressure and velocities.
Disadvantage is higher order numerical schemes
with order higher than second order will be
difficult.
For the unsteady problems, also if you are
discretising using forward time then this
is known as explicit method where you have
only one unknown, where n plus 1 is the current
time step and n is the previous time step.
So, this is known as explicit method.
So, only one unknown is there and you can
have in the right hand side all known terms
at the time level n.
But if you use backward time discretization
method for the temporal gradient then it is
known as implicit method, where you have more
than one unknowns.
You can see it is n plus 1 and here also n
plus 1, so obviously you have more than one
unknowns at n plus 1 time level, which is
the present time level.
So, this is known as implicit method.
So, in explicit method as it is only one unknown
it is easy to solve, but where in implicit
method where you have more than unknowns so
you have to use some numerical techniques,
sorry numerical solvers to solve these equations.
So, for solving this discretization equation,
you can use these iterative methods, one is
Jacobi method, other is Gauss Seidel method,
we will discuss in detail later, Successive
Over-Relaxation, Alternative direction implicit
method, so these are some iterative methods.
We have some other methods where which are
known as conjugate gradient methods, biconjugate
gradient methods and you can also use multigrid.
So, you can see that when you are solving
some problems using CFD, first you identify
the right approximation OK and write down
the governing equations.
So, identification of right approximation
means, whether it is Viscous or inviscous
inviscid, because you can write the governing
equation accordingly, whether laminar or turbulent
OK, incompressible or compressible, single-phase
or multi-phase, so accordingly you first identify
the right approximation and write the governing
equations.
Then you identify the right solution method
OK, so, which discretization scheme you want
to use, say finite difference method, finite
element method or finite volume method, whether
you can use want to use structured or unstructured
grid OK and what is the order of accuracy
you will use, temporal and spatial both.
So, accordingly you need to discretise these
partial differential equations.
Then in pre-processing stage, generate the
computational grid, because at discrete points
you need to solve this discretized equation,
so depending on your choice whether structured
or unstructured grid you generate the computational
grid, then in pre-processing stage you assign
the boundary conditions OK, if it is time
varying then with solutions you need to apply
the boundary conditions.
Then set initial conditions OK for the unsteady
problem.
If it is a steady problem then you need to
have the guess solution at starting while
starting the iterative method.
Then once all these are done then you compile
the code, so if there are some errors then
you fix the bug, then prepare input parameters,
then you solve this, run the code OK, monitor
the solutions.
So, whether your error is decreasing with
iteration or time that you check and monitor.
Once you get the convergence then you get
the results.
But, results you will get in terms of numbers
only.
So, at discrete points you will have the values
OK of particular variables.
So, those you collect and organize the data,
then you use some post processing software
and analyse the results.
Now, once you post process it, first you need
to verify the solution, what is verification?
Whether these are physically correct or not.
Because if you are solving a fluid flow problem
in a channel, let us say the flow is taking
place from left to right, but if you are getting
the solution from right to left, the velocity
is coming from right to left , then obviously
it is not physically correct.
So, based on your problem whatever you have
chosen, so you check whether the results are
physically correct or not.
So, do the results make sense?
Are the trends right?
Does it agree with previous calculation on
similar configurations?
So, that you verify.
Once you get it, then you solve a known problem,
which already the solution is available in
literature, so that is known as validation
OK.
So, when you write the solver first time,
you need to know whether the solver is giving
correct result or not, so to test it you need
to solve a known problem which is available
in the literature.
So, does the results or the aspect of the
results agree with theory or experiments?
So, you can have some numerical or experimental
results available in literature.
So, qualitatively you can check first whether
these are matching or not, but you need to
verify also quantitatively.
That means you need to find the velocity distribution
at a particular line or a particular area
then you can compare it with the available
results in literature OK, whether it is numerical
or experimental but need to compare, or any
other values like drag coefficient or lift
coefficient or the moment coefficient or the
shear stresses, distribution along a wall.
So, all those things quantitatively you need
to compare with the with your results and
the results available in the literature to
verify your solver so that you will be confident
that your code is correctly written and there
is no bugs.
So, there are different types of CFD codes
available like commercial CFD codes ANSYS
Fluent, Star-CD, CFX, then COMSOL it is a
very multi physics software, so ANSYS Fluent,
Star-CD these are written in using finite
volume method, but COMSOL is a written using
finite element method.
You have some public domain software like
PHI3D, HYDRO, OpenFOAM.
And for this solving the multi-phase flow
you have Gerris and Basilisk, so that are
also available and these are free, you can
download and you can use it.
And other CFD software includes the grid generation
software, obviously you need to generate the
grid before solving the equations.
And there are some software like Gridgen,
Gambit, ICEM CFD, these are some commercial
softwares available but also some open source
software is there like Salome, so you can
generate structured and unstructured grid
and it is having the graphical user interphase
also to generate the grid.
And to post process the results you have flow
visualization software OK, so Tecplot, FieldView,
you can use to post process the results and
visualize the results, so these are some commercial
and open source software we discussed.
So, in today’s lecture, we have seen why
we need to use the computational fluid dynamics
and what are the procedures to solve any problem
using CFD.
We have also discussed some history of CFD,
then we have seen some application of CFD
in particular areas and later we have seen
the different type of grid OK, structured
grid and unstructured grid; we have also seen
different grid arrangement like co-located
grid and staggered grid.
After that, also, when you discretize the
equation, you will get the discretized algebraic
equations.
But you need to solve it right, so for solving
it you need some solver, so we have seen some
iterative solvers, like Jacobi, Gauss Seidel
or Successive-Over-Relaxation and also some
direct method like conjugate gradient method
or biconjugate gradient method.
Those things we will discuss more detail in
other modules.
And we have seen that when you solve a problem,
what are the steps you need to follow for
solving any problems.
Thank you.
