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Computational Fluid Dynamics Fundamentals Course 2

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Based on 674 ratings
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Dr Aidan Wimshurst

Welcome to Part 2 of my Computational Fluid Dynamics (CFD) fundamentals course. In this course, the concepts, derivations and examples from Part 1 are extended to look at 2D simulations, wall functions (U+, y+ and y*) and Dirichlet and Neumann boundary conditions. The course starts from first principles and you will rapidly develop working CFD solutions using the Excel sheets, MATLAB code and Python source code provided (you can complete the course with either Excel, MATLAB or python). By the end of the course, you will understand the importance of heat flux balances, residuals and wall functions (y+, U+ and y*). This course also presents a unique working example for temperature wall functions (never seen before on the internet), to show you exactly how wall functions are employed by CFD solvers. No prior experience is required and no specific CFD code/coding experience is required.   You do not need ANSYS Fluent, OpenFOAM, Star CCM or any other CFD to use this course.

Read more

Welcome to Part 2 of my Computational Fluid Dynamics (CFD) fundamentals course. In this course, the concepts, derivations and examples from Part 1 are extended to look at 2D simulations, wall functions (U+, y+ and y*) and Dirichlet and Neumann boundary conditions. The course starts from first principles and you will rapidly develop working CFD solutions using the Excel sheets, MATLAB code and Python source code provided (you can complete the course with either Excel, MATLAB or python). By the end of the course, you will understand the importance of heat flux balances, residuals and wall functions (y+, U+ and y*). This course also presents a unique working example for temperature wall functions (never seen before on the internet), to show you exactly how wall functions are employed by CFD solvers. No prior experience is required and no specific CFD code/coding experience is required.   You do not need ANSYS Fluent, OpenFOAM, Star CCM or any other CFD to use this course.

This course does not teach you how to use specific functionality in different CFD packages. Instead it provides fundamental understanding that you can use to understand how all CFD codes work behind the scenes and actually see the matrices as they are assembled and solved. You can use this understanding throughout your career in CFD to move between different CFD codes and understand the fundamental features that make them all work. This information is essential for any world-class CFD engineer.

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What's inside

Learning objectives

  • How to setup and structure a working cfd solution code from first principles (using excel, matlab or python)
  • How dirichlet and neumann boundary conditions are translated into cfd matrix equations
  • How to set up and solve 2d cfd solutions from first principles
  • How wall functions are actually employed by cfd codes
  • The utility of heat flux balances that can be generated from cfd solutions

Syllabus

Welcome and how to use this course

A short introduction to the course, with instructions on how to best follow along with the course material.

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A quick announcement on the version control and featured updates for this course.

The course starts off by reviewing the finite volume discretisation of the 1D heat diffusion equation. The formulation of Dirichlet and Neumann boundary conditions are then introduced and a comparison of the resulting matrix equations is provided

In this example problem, the 1D heat diffusion is solved along a 5m long bar. A fixed temperature of 200 degrees is applied at the right end and a fixed heat flux of 100 W/m2 is applied at the left end.

The heat diffusion equation is now extended to 2D. The extended form of the finite volume discretisation is introduced and the special treatment required for cells with multiple boundary faces is also introduced.

In this worked example, the heat diffusion equation is solved in a 2D plate. The plate has fixed temperatures of 100 degrees, 150 degrees, 200 degrees and 250 degrees applied to each of its faces.

The concept of wall functions and wall treatment is introduced comprehensively from first principles. The wall functions for the kinematic viscosity and thermal diffusivity are derived and their implementation in the finite volume method is presented.

The example problem from the first chapter (heat diffusion in a 1D bar) is now extended to include a temperature wall function at the right end.

A brief summary and final thoughts for the course.

Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Extends concepts from Part 1 to 2D simulations, wall functions, and boundary conditions, building upon prior knowledge for a deeper understanding
Develops working CFD solutions using Excel, MATLAB, or Python, offering flexibility for learners with different coding preferences and skill levels
Focuses on fundamental understanding applicable across different CFD codes, enabling learners to adapt and troubleshoot in various software environments
Presents a unique working example for temperature wall functions, offering insights into how CFD solvers handle heat transfer at boundaries
Requires completion of Part 1, which may pose a barrier for learners seeking a standalone introduction to CFD concepts

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Reviews summary

Cfd fundamentals: 2d & wall functions

Based on the course description and syllabus, learners would likely find this course focuses on extending Computational Fluid Dynamics (CFD) fundamentals to 2D simulations and introduces wall functions for turbulent flow. The course structure suggests a foundational approach, aiming to teach students how CFD solvers work from first principles rather than how to use specific commercial software like ANSYS Fluent or OpenFOAM. It appears the course offers multiple coding options, allowing students to develop solutions using Excel, MATLAB, or Python. Key topics covered include translating Dirichlet and Neumann Boundary Conditions into matrix equations and understanding heat flux balances.
Covers Dirichlet and Neumann BCs.
"...extended to look at...Dirichlet and Neumann boundary conditions."
"How Dirichlet and Neumann Boundary Conditions are translated into CFD matrix equations"
Use Excel, MATLAB, or Python.
"...you will rapidly develop working CFD solutions using the Excel sheets, MATLAB code and Python source code provided..."
"...you can complete the course with either Excel, MATLAB or python."
Extends concepts to 2D problems.
"...extend the concepts, derivations and examples from Part 1 to look at 2D simulations..."
"By the end of this section students will be able to derive from first principles and set up finite volume matrix equations in 2D"
Builds understanding of how CFD works.
"This course does not teach you how to use specific functionality in different CFD packages."
"Instead it provides fundamental understanding that you can use to understand how all CFD codes work behind the scenes..."
"...actually see the matrices as they are assembled and solved."
Detailed look at wall functions.
"...look at...wall functions (U+, y+ and y*)."
"This course also presents a unique working example for temperature wall functions..."
"Understand how wall functions (for high Reynolds number turbulent flow) are actually incorporated into CFD codes."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Computational Fluid Dynamics Fundamentals Course 2 with these activities:
Review Finite Volume Method
Reinforce your understanding of the finite volume method, which is crucial for understanding the numerical techniques used in CFD.
Browse courses on Finite Volume Method
Show steps
  • Review notes and examples from previous courses on numerical methods.
  • Work through practice problems involving finite volume discretization.
  • Compare and contrast finite volume with other discretization methods like finite difference and finite element.
Review 'Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics'
Deepen your understanding of the numerical methods used in CFD by studying a comprehensive textbook.
View Numerical Computation of Internal and External... on Amazon
Show steps
  • Read the chapters related to finite volume methods and boundary conditions.
  • Work through the example problems provided in the book.
  • Compare the book's approach to the concepts taught in the course.
Solve Boundary Condition Problems
Improve your ability to apply Dirichlet and Neumann boundary conditions by solving a variety of practice problems.
Show steps
  • Find or create a set of CFD problems with different boundary conditions.
  • Solve each problem by hand, setting up the matrix equations.
  • Verify your solutions using a simple CFD solver or calculator.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Create a CFD Resource Compilation
Improve your understanding of CFD by creating a compilation of useful resources and tools.
Show steps
  • Gather links to relevant websites, articles, and tutorials.
  • Organize the resources into categories such as solvers, pre-processing tools, and post-processing tools.
  • Write a brief description of each resource.
Implement 2D Heat Diffusion Solver
Solidify your understanding of 2D CFD by implementing your own heat diffusion solver from scratch.
Show steps
  • Design the data structures to represent the 2D domain and variables.
  • Implement the finite volume discretization for the 2D heat diffusion equation.
  • Implement Dirichlet and Neumann boundary conditions.
  • Solve the resulting system of equations using a suitable linear solver.
  • Visualize the temperature distribution.
Create a CFD Wall Function Explainer Video
Deepen your understanding of wall functions by creating an educational video explaining their purpose and implementation.
Show steps
  • Research and gather information about wall functions in CFD.
  • Write a script outlining the key concepts and steps.
  • Create visuals to illustrate the concepts.
  • Record and edit the video.
Review 'Turbulent Flows' by Stephen Pope
Expand your knowledge of turbulence modeling and wall functions by studying a classic textbook on turbulent flows.
View Turbulent Flows on Amazon
Show steps
  • Read the chapters related to wall functions and near-wall turbulence modeling.
  • Compare the book's approach to the concepts taught in the course.
  • Identify the limitations of the wall function approach.

Career center

Learners who complete Computational Fluid Dynamics Fundamentals Course 2 will develop knowledge and skills that may be useful to these careers:
Computational Fluid Dynamics Engineer
A Computational Fluid Dynamics Engineer uses simulation software to model the behavior of fluids. This course helps build a foundation in the fundamentals of how such simulations are performed. It introduces the core mathematical concepts including finite volume matrix equations. The course also investigates heat flux balances, and wall functions such as U+, y+, and y*, which are crucial for accurate modeling of fluid flow near walls. The practical application of boundary conditions, such as Dirichlet and Neumann, are covered, which are essential for setting up real-world simulations. This course, with its emphasis on core concepts and practical implementation, helps a prospective Computational Fluid Dynamics Engineer understand the underlying math behind various CFD software packages.
See salaries and explore the career path for Computational Fluid Dynamics Engineer
Fluid Dynamics Modeler
A Fluid Dynamics Modeler develops numerical models to simulate and analyze fluid flow behavior. This course is directly relevant, as it explains how to construct computational fluid dynamics solutions from first principles. The course explicitly covers setting up and solving 2D solutions while also investigating wall functions and boundary conditions. It also introduces heat flux balances. This knowledge helps a Fluid Dynamics Modeler to understand and improve existing models or create new ones. The course also discusses how to implement these models using common tools, like Excel, MATLAB, or Python.
See salaries and explore the career path for Fluid Dynamics Modeler
Research Scientist
A Research Scientist in fluid dynamics or heat transfer often conducts fundamental studies of complex systems. This course can be instrumental in gaining a deep understanding of the computational methods used in this field. It covers the derivation and implementation of finite volume matrix equations for heat transfer, including the application of Dirichlet and Neumann boundary conditions. The course's emphasis on wall treatment and functions, such as y+, U+, and y*, helps to understand how those are incorporated into CFD models. Also, the practical approach of creating working CFD solutions in Excel, MATLAB, or Python can be useful for research tasks. A Research Scientist can employ techniques learned from this course to develop and validate numerical models of fluid flow in their research.
See salaries and explore the career path for Research Scientist
Simulation Engineer
A Simulation Engineer uses modeling software to simulate the behavior of complex systems. This course provides a foundation in the underlying principles of computational fluid dynamics and heat transfer which are vital for this role. The course explores how to formulate and solve 2D CFD solutions starting from first principles. It provides a deep understanding of the numerical methods employed in simulation software, including finite volume methods, and how boundary conditions such as Dirichlet and Neumann are applied. This course also offers insights on handling wall functions like y+, U+, and y*, relevant in simulating fluid dynamics in various scenarios such as heat transfer analysis. A Simulation Engineer will find that this course enables them to better design simulations and to interpret results effectively.
See salaries and explore the career path for Simulation Engineer
Thermal Engineer
A Thermal Engineer focuses on heat transfer and thermal management in various systems. This course provides an excellent foundation in the numerical methods used to simulate heat transfer phenomena. It explores the finite volume discretization of the heat diffusion equation, along with Dirichlet and Neumann boundary conditions, which are critical for modeling thermal systems. The course's focus on heat flux balances and wall functions, such as U+, y+, and y*, as they pertain to thermal systems, are useful skills for a Thermal Engineer. The course's coverage of 2D heat diffusion and the implementation of temperature wall functions is especially valuable. A Thermal Engineer may find this course instrumental in developing a deeper understanding of the underlying principles behind thermal simulation software.
See salaries and explore the career path for Thermal Engineer
Energy Systems Engineer
An Energy Systems Engineer works on designing and optimizing energy systems, often involving heat transfer. This course helps in understanding the underlying principles of modeling energy systems. It discusses how to set up 2D CFD solutions and provides insights into heat flux balances, and wall functions, such as y+, U+, and y* . The course also covers how boundary conditions, like Dirichlet and Neumann, affect the simulation. The knowledge gained from this course is useful to an Energy Systems Engineer in improving the efficiency and performance of energy systems through simulation.
See salaries and explore the career path for Energy Systems Engineer
Aerospace Engineer
An Aerospace Engineer designs and develops aircraft and spacecraft. This course provides a fundamental understanding of computational fluid dynamics that is useful in this role. The course delves into the setup of CFD solutions from first principles and the application of boundary conditions such as Dirichlet and Neumann, which are important in aerospace design simulations. The course covers heat flux balances and wall functions, such as y+, U+, and y*, which are crucial for understanding aerodynamic and thermal behavior. An Aerospace Engineer can leverage the knowledge gained from this course to create accurate models of fluid flow and heat transfer for use in the design of aerospace vehicles.
See salaries and explore the career path for Aerospace Engineer
Mechanical Engineer
A Mechanical Engineer works on the design, development, manufacturing, and testing of mechanical devices and systems. This course can be useful in understanding the behavior of fluids and heat transfer within mechanical systems using a numerical approach that builds working solutions. The course delves into the formulation of matrix equations for heat diffusion, along with the use of Dirichlet and Neumann boundary conditions. Mechanical Engineers may find this course helpful in understanding how wall functions, such as y+, U+, and y*, are implemented in CFD codes. Specifically, understanding the finite volume method and how it relates to complex geometries and heat transfer can be instrumental for a Mechanical Engineer in designing more efficient mechanical systems.
See salaries and explore the career path for Mechanical Engineer
Automotive Engineer
An Automotive Engineer works on the design and development of vehicles, which involves understanding aerodynamics and thermal management. This course provides a solid foundation for understanding the computational methods used in modeling fluid dynamics and heat transfer, which are crucial for automotive applications. The course includes instruction on setting up 2D CFD simulations and implementing relevant boundary conditions. This course discusses wall functions such as U+, y+, and y+, which are important for modeling airflow around vehicles and heat transfer in engines. An Automotive Engineer can use the fundamental knowledge gained here to design more efficient and aerodynamic vehicles.
See salaries and explore the career path for Automotive Engineer
Product Development Engineer
A Product Development Engineer is involved in creating and improving products, often using simulation to test. This course helps one understand the fundamental mathematics behind such simulation software which can serve as an advantage. The course helps build a foundation for modeling complex physical phenomena like heat transfer and fluid dynamics. The course explores the implementation of boundary conditions and wall functions such as U+, y+, and y*, used in CFD. The understanding of matrix equations that is built in this course helps a Product Development Engineer appreciate how such models are constructed and how to use them in product design for various applications.
See salaries and explore the career path for Product Development Engineer
Engineering Consultant
An Engineering Consultant provides expert advice on engineering projects, often involving complex simulations. This course helps develop a deep understanding of the fundamentals of computational fluid dynamics and heat transfer. The course specifically teaches how to derive and implement finite volume matrix equations along with boundary conditions. It also explains how to create a working 2D simulation from first principles, including wall functions y+, U+, and y*. This knowledge may be helpful in evaluating the validity of simulations. An Engineering Consultant may benefit from the understanding of the underlying principles discussed in this course.
See salaries and explore the career path for Engineering Consultant
Process Engineer
A Process Engineer designs and optimizes industrial processes, many of which involve fluid flow and heat transfer. This course may be useful for understanding the numerical methods used to simulate and optimize these processes. It provides a thorough introduction to the finite volume method, including an analysis of Dirichlet and Neumann conditions, along with wall functions like y+, U+, and y*. The course's practical approach of creating working CFD solutions may be helpful for a process engineer. This course may be useful to Process Engineers by providing a better understanding of the underlying mechanics behind process simulation software.
See salaries and explore the career path for Process Engineer
Biomedical Engineer
A Biomedical Engineer applies engineering principles to healthcare and medicine. This course may be helpful for those interested in modeling biological fluid flows or heat transfer processes. The course explores the finite volume method, Dirichlet and Neumann boundary conditions, and how to set up 2D simulations. It also covers wall functions, such as y+, U+, and y*, which may be useful in understanding biological flows. The skills and knowledge gained from this course may be useful for a Biomedical Engineer in simulating biological processes and medical devices involving fluid flow and heat transfer.
See salaries and explore the career path for Biomedical Engineer
Industrial Engineer
An Industrial Engineer focuses on optimizing complex systems and processes, often involving fluid flow and heat transfer. This course may be useful for those interested in understanding and improving processes that rely on such phenomena through modeling. It provides a background in the finite volume method, including the modeling of heat diffusion with Dirichlet and Neumann boundary conditions, and wall functions. This course can be helpful to an Industrial Engineer in analyzing and improving production processes by understanding the principles of simulation software.
See salaries and explore the career path for Industrial Engineer
Data Scientist
A Data Scientist analyzes large datasets to extract insights and make predictions. This course may be useful as it utilizes numerical methods for solving complex engineering problems. The course covers using tools like excel, python, and MATLAB to develop and solve matrix equations which is often used in data science. A Data Scientist will find the course's approach to structuring working code to be helpful. The course also covers heat flux balances and wall functions which helps a data scientist gain additional knowledge of mathematical methods which can be applied to other domains.
See salaries and explore the career path for Data Scientist

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Computational Fluid Dynamics Fundamentals Course 2.
Cover image
Numerical Computation of Internal and External Flows
Save
Provides a comprehensive overview of the fundamental principles and numerical techniques used in CFD. It covers finite volume methods, boundary conditions, and turbulence modeling in detail. It valuable resource for understanding the theoretical underpinnings of CFD and complements the practical aspects covered in the course. This book is often used as a textbook in graduate-level CFD courses.
Numerical Computation of Internal and External Flows
Paperback
Check
Numerical Computation of Internal and External Flows
Kindle Edition
Check
Cover image
Turbulent Flows
Save
Provides a comprehensive and rigorous treatment of turbulent flows, including detailed explanations of wall functions and turbulence modeling. While advanced, it offers a deeper understanding of the underlying physics and assumptions behind the wall functions used in CFD. This book is more valuable as additional reading for those seeking a deeper understanding of turbulence.
Turbulent Flows
Paperback
$$$
(中文) Turbulent flow(Chinese Edition)
Paperback
$$$
Turbulent Flows
Kindle Edition
$$$

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Rating
4.8 Filled star Filled star Filled star Filled star Half star
Effort
2.5 total hours
Via
Udemy
Instructor
Dr Aidan Wimshurst
Language
English
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Extends concepts from Part 1 to 2D simulations, wall functions, and boundary conditions, building upon prior knowledge for a deeper understanding
Develops working CFD solutions using Excel, MATLAB, or Python, offering flexibility for learners with different coding preferences and skill levels
Focuses on fundamental understanding applicable across different CFD codes, enabling learners to adapt and troubleshoot in various software environments
Presents a unique working example for temperature wall functions, offering insights into how CFD solvers handle heat transfer at boundaries
Requires completion of Part 1, which may pose a barrier for learners seeking a standalone introduction to CFD concepts
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