SlideShare a Scribd company logo
6
Most read
12
Most read
19
Most read
Approaches in CFD
Author : Parham Sagharichi Ha
Agenda
▪ Computational Fluid Dynamics or CFD
▪ Applications, Advantages, disadvantages of CFD
▪ Process in CFD
▪ Popular discretization approaches in CFD
▪ Finite difference method (FDM)
▪ Finite volume method (FVM)
▪ Finite element method (FEM)
Computational Fluid Dynamics
▪ Computational Fluid Dynamics or CFD is the analysis of systems
involving fluid flow, heat transfer and associated phenomenas
such as chemical reactions by means of computer based
simulation.
Applications of CFD
▪ Aerodynamics of aircraft and vehicles: lift and drag.
▪ Hydrodynamics of ship.
▪ Power Plant: Gas turbines.
▪ Chemical Process Engineering: mixing and separation.
▪ Marine engineering: loads on off-shore structure.
▪ Environmental Engineering: Distribution of pollutants
▪ Biomedical Engineering: blood flows through arteries
and veins.
Advantages of CFD
▪ Study specific terms in the governing equations in a detailed
fashion.
▪ Complements experimental and analytical.
▪ CFD substantially reduces lead times and cost in design.
▪ Simulating flow conditions that are not reproducible in
experimental test.
▪ Provide rather detailed, visualized and comprehensive information
as compared to other methods.
Disadvantages of CFD
▪ A large amount of processing power is nedded to run some test
case.
▪ If the processing of reading & writing to the CFD packages
slow,then the whoule solution process is slowed down.
Process in CFD
▪ In order to provide easy access to, almost all current commercial
and some shareware CFD package include user friendly Graphical
User Interface(GUI) applications. The codes that provide a
complete CFD analysis consists of three main elements :
1. Pre-Processor.
2. Solver.
3. Post-Processor.
Pre - Processor
▪ Pre-Processing consists of input to flow problem by user and
transformation to a form usable by the solver.
1. Defining geometry of interest; Computational Domain.
2. Sub Division of domain into a number of overlapping sub
domain; a grids(mesh) cell.
3. Selection of physical and chemical phenomena that needs to
be modeled.
4. Defining fluid properties.
5. Specifying of Boundary Conditions.
Solver
▪ In outline the numerical methods that form the
basis of the solver perform the following steps:
1. Approximation of unknown flow variables by
means of functions.
2. Discretization and mathematical manipulations.
3. Solutions to algebraic equations.
Post - Processor
▪ Modern CFD packages have outstanding data visualization tools, which
includes:
1. Domain geometry and grid display.
2. Vector plots.
3. Lines and shaded contour plots.
4. 2D and 3D surface plots.
5. Particle Tracking.
6. View manipulation.
7. Colour Post script output.
Popular discretization approaches in CFD
▪ Finite Difference Method
▪ Finite Volume Method(ANSYS FLUENT)
▪ Finite Element Method
Finite difference method (FDM)
▪ FDM is created from basic definition of differentiation that is
𝑑𝑓
𝑑𝑥
=
𝑓 𝑥 + ℎ − 𝑓(𝑥)
ℎ
▪ In numerical analysis, its not possible to divide a number by "0" so
"zero" means a small number. So FDM is similar to differential
calculus but it has killed the heart that is limit tenda to "zero". So
in most of the cases accuracy of FDM increases with refining grid.
Easy method but not reliable for conservative differential equations
and solutions having shocks. Tough to implement in complex
geometry where it needs complex mapping and mapping makes
governing equation even tougher. Extending to higher order
accuracy is very simple.
Finite difference method (FDM)
▪ A finite difference method (FDM) discretization is based upon the
differential form of the PDE to be solved. Each derivative is
replaced with an approximate difference formula (that can generally
be derived from a Taylor series expansion). The computational
domain is usually divided into hexahedral cells (the grid), and the
solution will be obtained at each nodal point. The FDM is easiest to
understand when the physical grid is Cartesian, but through the use
of curvilinear transforms the method can be extended to domains
that are not easily represented by brick-shaped elements. The
discretization results in a system of equation of the variable at
nodal points, and once a solution is found, then we have a discrete
representation of the solution.
Finite volume method (FVM)
▪ It is a numerical tool that is borrowed from calculus of variation. There are lot of
types of FEM like point collocation method, sub-domain method etc. Here they
assume some trial function and multiply that trial function with weighting
function . In Galerkins method the trial function itself weighting function.
Different methods follow different ways in weighting. Then this weighting
function is multiplied with trial function then integrated over the control volume
( weak form) and equated to zero (This procedure will differ for different types of
FEM but theme is same). Then we get one set of algebraic equations. Solving that
will give solution. Here we are working only in error and differential equation
some times conservative law may be violated. This method is more accurate than
FVM and FDM. Ideal for linear PDEs, expensive and complex for non-linear
PDEs. Here higher order accuracy is achieved by using higher order basis (i.e)
shape functions. Extending to higher order accuracy is relatively complex than
FVM and FDM. Higher order accurate calculations are expensive in computation
and Mathematical formulation especially for non-linear PDEs. Mostly suitable for
Heat transfer, Structural mechanics, vibrational analysis etc.
Finite volume method (FVM)
▪ A finite volume method (FVM) discretization is based upon an integral
form of the PDE to be solved (e.g. conservation of mass, momentum, or
energy). The PDE is written in a form which can be solved for a given
finite volume (or cell). The computational domain is discretized into finite
volumes and then for every volume the governing equations are solved.
The resulting system of equations usually involves fluxes of the conserved
variable, and thus the calculation of fluxes is very important in FVM. The
basic advantage of this method over FDM is it does not require the use of
structured grids, and the effort to convert the given mesh in to structured
numerical grid internally is completely avoided. As with FDM, the
resulting approximate solution is a discrete, but the variables are typically
placed at cell centers rather than at nodal points. This is not always true,
as there are also face-centered finite volume methods. In any case, the
values of field variables at non-storage locations (e.g. vertices) are
obtained using interpolation.
Finite element method (FEM)
▪ This is similar to FDM but. It didn't kill the theme of
differentiation because we are integrating the differential equation
over a control volume and discretizing the domain. Since we have
integrated the differential equation discetization is mathematically
a valid one. It can be loosely viewed as FEM but weight here used is
1. Here fluxes are integrated and resultant is set to zero, so flux is
conserved. Can handle almost any PDEs and complex domain.
Interpolation is done from face to centre will reduce the accuracy of
this process. Here accuracy is based on order of polynomial used.
FVM can also produce any order accurate numerical solution similar
to FDM but more expensive than FDM Aero acoustic problems use
FVM about 11th order schemes such schemes are rarely used even in
DNS and LES. Ideal for Fluid mechanics.
Finite element method (FEM)
▪ A finite element method (FEM) discretization is based upon a
piecewise representation of the solution in terms of specified basis
functions. The computational domain is divided up into smaller
domains (finite elements) and the solution in each element is
constructed from the basis functions. The actual equations that are
solved are typically obtained by restating the conservation equation
in weak form: the field variables are written in terms of the basis
functions, the equation is multiplied by appropriate test functions,
and then integrated over an element. Since the FEM solution is in
terms of specific basis functions, a great deal more is known about
the solution than for either FDM or FVM. This can be a double-
edged sword, as the choice of basis functions is very important and
boundary conditions may be more difficult to formulate. Again, a
system of equations is obtained (usually for nodal values) that must
be solved to obtain a solution.
Result
▪ Comparison of the three methods is difficult, primarily due to the
many variations of all three methods. FVM and FDM provide
discrete solutions, while FEM provides a continuous (up to a point)
solution. FVM and FDM are generally considered easier to program
than FEM, but opinions vary on this point. FVM are generally
expected to provide better conservation properties, but opinions
vary on this point also. If you are trying to decide which method to
use, then the best path is probably found by consulting the
literature in the specific problem area.
Do you have any questions ?
Parham Sagharichi Ha

More Related Content

PPTX
Fundamentals of Computational Fluid Dynamics
PPT
CFD Concepts.ppt
PPT
Introduction to Computational Fluid Dynamics (CFD)
PDF
finite volume method
PPTX
Computational Fluid Dynamics (CFD)
PDF
Finite Volume Method Advanced Numerical Analysis by Md.Al-Amin
PDF
Fluent-Intro_15.0_L07_Turbulence.pdf
PPTX
CFD Introduction using Ansys Fluent
Fundamentals of Computational Fluid Dynamics
CFD Concepts.ppt
Introduction to Computational Fluid Dynamics (CFD)
finite volume method
Computational Fluid Dynamics (CFD)
Finite Volume Method Advanced Numerical Analysis by Md.Al-Amin
Fluent-Intro_15.0_L07_Turbulence.pdf
CFD Introduction using Ansys Fluent

What's hot (20)

PDF
Introduction to cfd
PDF
ME6603 - FINITE ELEMENT ANALYSIS UNIT - I NOTES AND QUESTION BANK
PPT
Finite Element Analysis - UNIT-1
PPTX
FEM and it's applications
PDF
CFD : Modern Applications, Challenges and Future Trends
PPT
PPTX
Meshing Techniques.pptx
PPT
Introduction to finite element method(fem)
PPTX
INTRODUCTION TO FINITE ELEMENT ANALYSIS
PDF
ME6603 - FINITE ELEMENT ANALYSIS
PPT
Cfd notes 1
PPTX
Finite Element Methods
PDF
ME6603 - FINITE ELEMENT ANALYSIS UNIT - III NOTES AND QUESTION BANK
PDF
ME6603 - FINITE ELEMENT ANALYSIS UNIT - II NOTES AND QUESTION BANK
PPT
FLUID MECHANICS - COMPUTATIONAL FLUID DYNAMICS (CFD)
PPT
CFD & ANSYS FLUENT
PPTX
Introduction to FEA
PPT
ansys presentation
PPT
Finite element method
PPTX
Finite Element Method
Introduction to cfd
ME6603 - FINITE ELEMENT ANALYSIS UNIT - I NOTES AND QUESTION BANK
Finite Element Analysis - UNIT-1
FEM and it's applications
CFD : Modern Applications, Challenges and Future Trends
Meshing Techniques.pptx
Introduction to finite element method(fem)
INTRODUCTION TO FINITE ELEMENT ANALYSIS
ME6603 - FINITE ELEMENT ANALYSIS
Cfd notes 1
Finite Element Methods
ME6603 - FINITE ELEMENT ANALYSIS UNIT - III NOTES AND QUESTION BANK
ME6603 - FINITE ELEMENT ANALYSIS UNIT - II NOTES AND QUESTION BANK
FLUID MECHANICS - COMPUTATIONAL FLUID DYNAMICS (CFD)
CFD & ANSYS FLUENT
Introduction to FEA
ansys presentation
Finite element method
Finite Element Method
Ad

Viewers also liked (11)

PPTX
Comparativa LIO trifocales LISA TRI FINEVISION PANOPTIX
PPTX
Meio Ambiente - Dicas e truques de impress
PPT
10. apresentação cras gloria
PPTX
Doenças respiratórias nos idosos
DOC
Introdução miiase
PDF
Banking Consumers: 5 Core Segments and How to Reach Them
DOC
Tcc completo e A INCLUSÃO DA PESSOA COM DEFICIÊNCIA NO MERCADO DE TRABALHOrev...
PPTX
Finite element method
PDF
Reações de Ácidos Carboxílicos e Derivados
PPT
Drug Abuse and Addiction
PDF
Mecanica exercicios resolvidos
Comparativa LIO trifocales LISA TRI FINEVISION PANOPTIX
Meio Ambiente - Dicas e truques de impress
10. apresentação cras gloria
Doenças respiratórias nos idosos
Introdução miiase
Banking Consumers: 5 Core Segments and How to Reach Them
Tcc completo e A INCLUSÃO DA PESSOA COM DEFICIÊNCIA NO MERCADO DE TRABALHOrev...
Finite element method
Reações de Ácidos Carboxílicos e Derivados
Drug Abuse and Addiction
Mecanica exercicios resolvidos
Ad

Similar to Fvm fdm-fvm (20)

PPTX
discretization_methods.pptx. H
PPTX
Computational Fluid Dynamics (CFD)
PDF
Part 2 CFD basics Pt 2(1).pdf
PDF
A Comprehensive Introduction of the Finite Element Method for Undergraduate C...
PPT
Fluent and Gambit Workshop
PDF
Computational fluid dynamics (cfd)
PDF
In tech finite-element_analysis_of_the_direct_drive_pmlom
PPTX
UNIT - 4 CAE AND CFD approach of future mobility
PDF
Lecture 1 velmurugan
PDF
Finite Volume Method Powerful Means Of Engineering Design Radostina Petrova
PPTX
Summer Training Ansys presentation.pptx
PPTX
HOME ASSIGNMENT.pptxcfccfggcccgggvvvvgggg
PPTX
introduction to CFD - Siemens Starccm Community
PPTX
compuatational fluid dynamics information
PPT
cfdht-fvm-unit3.ppt
PPTX
HOME ASSIGNMENT omar ali.pptx
PPTX
Solution of engineering problems
PDF
The finite element method basic concepts and applications 2nd ed Edition Pepper
discretization_methods.pptx. H
Computational Fluid Dynamics (CFD)
Part 2 CFD basics Pt 2(1).pdf
A Comprehensive Introduction of the Finite Element Method for Undergraduate C...
Fluent and Gambit Workshop
Computational fluid dynamics (cfd)
In tech finite-element_analysis_of_the_direct_drive_pmlom
UNIT - 4 CAE AND CFD approach of future mobility
Lecture 1 velmurugan
Finite Volume Method Powerful Means Of Engineering Design Radostina Petrova
Summer Training Ansys presentation.pptx
HOME ASSIGNMENT.pptxcfccfggcccgggvvvvgggg
introduction to CFD - Siemens Starccm Community
compuatational fluid dynamics information
cfdht-fvm-unit3.ppt
HOME ASSIGNMENT omar ali.pptx
Solution of engineering problems
The finite element method basic concepts and applications 2nd ed Edition Pepper

Recently uploaded (20)

PPTX
bas. eng. economics group 4 presentation 1.pptx
PPTX
web development for engineering and engineering
PPTX
UNIT 4 Total Quality Management .pptx
PPTX
CARTOGRAPHY AND GEOINFORMATION VISUALIZATION chapter1 NPTE (2).pptx
PDF
Operating System & Kernel Study Guide-1 - converted.pdf
PPT
Project quality management in manufacturing
PPTX
Foundation to blockchain - A guide to Blockchain Tech
PDF
Model Code of Practice - Construction Work - 21102022 .pdf
PDF
The CXO Playbook 2025 – Future-Ready Strategies for C-Suite Leaders Cerebrai...
PDF
BMEC211 - INTRODUCTION TO MECHATRONICS-1.pdf
PPTX
M Tech Sem 1 Civil Engineering Environmental Sciences.pptx
PPTX
Geodesy 1.pptx...............................................
PPTX
Sustainable Sites - Green Building Construction
PPTX
IOT PPTs Week 10 Lecture Material.pptx of NPTEL Smart Cities contd
PPTX
Internet of Things (IOT) - A guide to understanding
PDF
Mohammad Mahdi Farshadian CV - Prospective PhD Student 2026
PDF
keyrequirementskkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
PPTX
Infosys Presentation by1.Riyan Bagwan 2.Samadhan Naiknavare 3.Gaurav Shinde 4...
PPTX
CH1 Production IntroductoryConcepts.pptx
PPTX
MCN 401 KTU-2019-PPE KITS-MODULE 2.pptx
bas. eng. economics group 4 presentation 1.pptx
web development for engineering and engineering
UNIT 4 Total Quality Management .pptx
CARTOGRAPHY AND GEOINFORMATION VISUALIZATION chapter1 NPTE (2).pptx
Operating System & Kernel Study Guide-1 - converted.pdf
Project quality management in manufacturing
Foundation to blockchain - A guide to Blockchain Tech
Model Code of Practice - Construction Work - 21102022 .pdf
The CXO Playbook 2025 – Future-Ready Strategies for C-Suite Leaders Cerebrai...
BMEC211 - INTRODUCTION TO MECHATRONICS-1.pdf
M Tech Sem 1 Civil Engineering Environmental Sciences.pptx
Geodesy 1.pptx...............................................
Sustainable Sites - Green Building Construction
IOT PPTs Week 10 Lecture Material.pptx of NPTEL Smart Cities contd
Internet of Things (IOT) - A guide to understanding
Mohammad Mahdi Farshadian CV - Prospective PhD Student 2026
keyrequirementskkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Infosys Presentation by1.Riyan Bagwan 2.Samadhan Naiknavare 3.Gaurav Shinde 4...
CH1 Production IntroductoryConcepts.pptx
MCN 401 KTU-2019-PPE KITS-MODULE 2.pptx

Fvm fdm-fvm

  • 1. Approaches in CFD Author : Parham Sagharichi Ha
  • 2. Agenda ▪ Computational Fluid Dynamics or CFD ▪ Applications, Advantages, disadvantages of CFD ▪ Process in CFD ▪ Popular discretization approaches in CFD ▪ Finite difference method (FDM) ▪ Finite volume method (FVM) ▪ Finite element method (FEM)
  • 3. Computational Fluid Dynamics ▪ Computational Fluid Dynamics or CFD is the analysis of systems involving fluid flow, heat transfer and associated phenomenas such as chemical reactions by means of computer based simulation.
  • 4. Applications of CFD ▪ Aerodynamics of aircraft and vehicles: lift and drag. ▪ Hydrodynamics of ship. ▪ Power Plant: Gas turbines. ▪ Chemical Process Engineering: mixing and separation. ▪ Marine engineering: loads on off-shore structure. ▪ Environmental Engineering: Distribution of pollutants ▪ Biomedical Engineering: blood flows through arteries and veins.
  • 5. Advantages of CFD ▪ Study specific terms in the governing equations in a detailed fashion. ▪ Complements experimental and analytical. ▪ CFD substantially reduces lead times and cost in design. ▪ Simulating flow conditions that are not reproducible in experimental test. ▪ Provide rather detailed, visualized and comprehensive information as compared to other methods.
  • 6. Disadvantages of CFD ▪ A large amount of processing power is nedded to run some test case. ▪ If the processing of reading & writing to the CFD packages slow,then the whoule solution process is slowed down.
  • 7. Process in CFD ▪ In order to provide easy access to, almost all current commercial and some shareware CFD package include user friendly Graphical User Interface(GUI) applications. The codes that provide a complete CFD analysis consists of three main elements : 1. Pre-Processor. 2. Solver. 3. Post-Processor.
  • 8. Pre - Processor ▪ Pre-Processing consists of input to flow problem by user and transformation to a form usable by the solver. 1. Defining geometry of interest; Computational Domain. 2. Sub Division of domain into a number of overlapping sub domain; a grids(mesh) cell. 3. Selection of physical and chemical phenomena that needs to be modeled. 4. Defining fluid properties. 5. Specifying of Boundary Conditions.
  • 9. Solver ▪ In outline the numerical methods that form the basis of the solver perform the following steps: 1. Approximation of unknown flow variables by means of functions. 2. Discretization and mathematical manipulations. 3. Solutions to algebraic equations.
  • 10. Post - Processor ▪ Modern CFD packages have outstanding data visualization tools, which includes: 1. Domain geometry and grid display. 2. Vector plots. 3. Lines and shaded contour plots. 4. 2D and 3D surface plots. 5. Particle Tracking. 6. View manipulation. 7. Colour Post script output.
  • 11. Popular discretization approaches in CFD ▪ Finite Difference Method ▪ Finite Volume Method(ANSYS FLUENT) ▪ Finite Element Method
  • 12. Finite difference method (FDM) ▪ FDM is created from basic definition of differentiation that is 𝑑𝑓 𝑑𝑥 = 𝑓 𝑥 + ℎ − 𝑓(𝑥) ℎ ▪ In numerical analysis, its not possible to divide a number by "0" so "zero" means a small number. So FDM is similar to differential calculus but it has killed the heart that is limit tenda to "zero". So in most of the cases accuracy of FDM increases with refining grid. Easy method but not reliable for conservative differential equations and solutions having shocks. Tough to implement in complex geometry where it needs complex mapping and mapping makes governing equation even tougher. Extending to higher order accuracy is very simple.
  • 13. Finite difference method (FDM) ▪ A finite difference method (FDM) discretization is based upon the differential form of the PDE to be solved. Each derivative is replaced with an approximate difference formula (that can generally be derived from a Taylor series expansion). The computational domain is usually divided into hexahedral cells (the grid), and the solution will be obtained at each nodal point. The FDM is easiest to understand when the physical grid is Cartesian, but through the use of curvilinear transforms the method can be extended to domains that are not easily represented by brick-shaped elements. The discretization results in a system of equation of the variable at nodal points, and once a solution is found, then we have a discrete representation of the solution.
  • 14. Finite volume method (FVM) ▪ It is a numerical tool that is borrowed from calculus of variation. There are lot of types of FEM like point collocation method, sub-domain method etc. Here they assume some trial function and multiply that trial function with weighting function . In Galerkins method the trial function itself weighting function. Different methods follow different ways in weighting. Then this weighting function is multiplied with trial function then integrated over the control volume ( weak form) and equated to zero (This procedure will differ for different types of FEM but theme is same). Then we get one set of algebraic equations. Solving that will give solution. Here we are working only in error and differential equation some times conservative law may be violated. This method is more accurate than FVM and FDM. Ideal for linear PDEs, expensive and complex for non-linear PDEs. Here higher order accuracy is achieved by using higher order basis (i.e) shape functions. Extending to higher order accuracy is relatively complex than FVM and FDM. Higher order accurate calculations are expensive in computation and Mathematical formulation especially for non-linear PDEs. Mostly suitable for Heat transfer, Structural mechanics, vibrational analysis etc.
  • 15. Finite volume method (FVM) ▪ A finite volume method (FVM) discretization is based upon an integral form of the PDE to be solved (e.g. conservation of mass, momentum, or energy). The PDE is written in a form which can be solved for a given finite volume (or cell). The computational domain is discretized into finite volumes and then for every volume the governing equations are solved. The resulting system of equations usually involves fluxes of the conserved variable, and thus the calculation of fluxes is very important in FVM. The basic advantage of this method over FDM is it does not require the use of structured grids, and the effort to convert the given mesh in to structured numerical grid internally is completely avoided. As with FDM, the resulting approximate solution is a discrete, but the variables are typically placed at cell centers rather than at nodal points. This is not always true, as there are also face-centered finite volume methods. In any case, the values of field variables at non-storage locations (e.g. vertices) are obtained using interpolation.
  • 16. Finite element method (FEM) ▪ This is similar to FDM but. It didn't kill the theme of differentiation because we are integrating the differential equation over a control volume and discretizing the domain. Since we have integrated the differential equation discetization is mathematically a valid one. It can be loosely viewed as FEM but weight here used is 1. Here fluxes are integrated and resultant is set to zero, so flux is conserved. Can handle almost any PDEs and complex domain. Interpolation is done from face to centre will reduce the accuracy of this process. Here accuracy is based on order of polynomial used. FVM can also produce any order accurate numerical solution similar to FDM but more expensive than FDM Aero acoustic problems use FVM about 11th order schemes such schemes are rarely used even in DNS and LES. Ideal for Fluid mechanics.
  • 17. Finite element method (FEM) ▪ A finite element method (FEM) discretization is based upon a piecewise representation of the solution in terms of specified basis functions. The computational domain is divided up into smaller domains (finite elements) and the solution in each element is constructed from the basis functions. The actual equations that are solved are typically obtained by restating the conservation equation in weak form: the field variables are written in terms of the basis functions, the equation is multiplied by appropriate test functions, and then integrated over an element. Since the FEM solution is in terms of specific basis functions, a great deal more is known about the solution than for either FDM or FVM. This can be a double- edged sword, as the choice of basis functions is very important and boundary conditions may be more difficult to formulate. Again, a system of equations is obtained (usually for nodal values) that must be solved to obtain a solution.
  • 18. Result ▪ Comparison of the three methods is difficult, primarily due to the many variations of all three methods. FVM and FDM provide discrete solutions, while FEM provides a continuous (up to a point) solution. FVM and FDM are generally considered easier to program than FEM, but opinions vary on this point. FVM are generally expected to provide better conservation properties, but opinions vary on this point also. If you are trying to decide which method to use, then the best path is probably found by consulting the literature in the specific problem area.
  • 19. Do you have any questions ? Parham Sagharichi Ha