An Introduction to Computational Fluid Dynamics from Udemy

A working knowledge of Computational Fluid Dynamics (CFD) is fast becoming a pre-requisite in many domains of engineering. In this course you will learn the fundamentals of this fascinating tool, including - but not limited to - the following concepts and associated applications:

- Using the Taylor series to tailor (no pun intended) approximations to derivatives of desired accuracy

- Discretizing differential equations and predicting the behavior (stability and accuracy) of these schemes

- The advantages and shortcomings of Explicit vs Implicit Methods

- Modified PDEs and types of error (Dissipative vs Dispersive)

- The intuition behind mathematical ideas like 'Substantial Derivative' and 'Divergence'

- Deriving the Navier-Stokes (NS) system of equations from first principles

- Manipulating and simplifying the NS equations to find the model suitable for your application

- Discretization of the NS equations using methods like MacCormack's scheme with artificial viscosity

- Using models of various fidelities (and attached Python code) to solve interesting problems like lid-driven cavities, shock tubes and shock-vortex interactions

- Extending the solvers presented to handle variations of canonical problems

As the title of the course suggests, this is meant to be an (extended) introduction, implying that several concepts have been deliberately (and regrettably) omitted, including, but not limited to:

- Transforming the NS equations to non-Cartesian coordinate systems

- Reynolds-averaging and turbulence modeling

- Large/Detached Eddy Simulations

- Grid generation

Finally, if you think you'd derive some benefit from this course, but can't afford the price, reach out to me via email and I'll send you a customized free link, no questions asked.

What's inside

Learning objectives

Understand how to derive, manipulate and simplify the navier stokes equations
Discretize the fluid dynamical equations and predict the accuracy, stability and error of numerical schemes

Write, run, extend and validate cfd solvers
Apply lessons learned to a handful of insightful applications like shock tubes and lid-driven cavities

Understand how to derive, manipulate and simplify the navier stokes equations
Discretize the fluid dynamical equations and predict the accuracy, stability and error of numerical schemes
Write, run, extend and validate cfd solvers
Apply lessons learned to a handful of insightful applications like shock tubes and lid-driven cavities

Syllabus

Course Overview and a brief walkthrough of the history of CFD

Course Overview

A (Very) Brief History of CFD

Learn how to use the Taylor series to construct derivatives of desired accuracy

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Covers the Navier-Stokes equations from first principles, which is fundamental knowledge for students in mechanical, aerospace, and chemical engineering

Explores the advantages and shortcomings of explicit versus implicit methods, which is essential for selecting appropriate numerical techniques in various engineering applications

Uses Python code to solve problems like lid-driven cavities, shock tubes, and shock-vortex interactions, which are standard benchmark problems in CFD

Omits transforming the Navier-Stokes equations to non-Cartesian coordinate systems, which may limit the applicability of the learned techniques to certain complex geometries

Omits Reynolds-averaging and turbulence modeling, which are essential for simulating turbulent flows commonly encountered in real-world engineering applications

Reviews summary

Rigorous introduction to computational fluid dynamics

Learners say this course offers an excellent and rigorous introduction to Computational Fluid Dynamics. The instructor is consistently praised for their clarity and expertise, making complex theoretical concepts understandable. Students appreciate the strong theoretical foundation provided, including the derivation of the Navier-Stokes equations, and the integration of practical Python coding examples. While the course is described as challenging and requires a solid background in mathematics and physics, reviewers find it highly rewarding and a top-notch starting point for the field. The overall sentiment is overwhelmingly positive, with reviews consistently recommending it over several years.

Focuses only on core introductory concepts.

"This is meant to be an (extended) introduction..."

"This is an introduction, doesn't cover advanced topics..."

"Good overview, but not deep dive into specifics like turbulence..."

"Covers the basics well..."

"A solid foundation, but you'll need more advanced courses..."

Demands solid math and physics skills.

"Requires a solid foundation in differential equations and linear algebra..."

"Don't underestimate the math required though!"

"Be prepared to spend significant time on the material, it's dense."

"You need a strong background in Calculus and Linear Algebra."

"Requires dedication and a good math background..."

Provides practical coding examples/solvers.

"The Python coding examples were particularly helpful for understanding practical applications."

"The Python scripts were useful..."

"The connection between theory and the practical Python implementations is well done."

"The practical coding assignments solidify understanding."

"The Python exercises are great for applying the theory."

Builds a solid understanding of CFD basics.

"This course provided me with an exceptional introduction..."

"A truly brilliant course that breaks down the daunting world of CFD..."

"Provides an excellent foundation."

"Really helped build a solid understanding."

"Comprehensive introduction covering the necessary math and physics fundamentals..."

Instructor is knowledgeable and clear.

"The instructor's expertise and ability to explain complex topics clearly were outstanding."

"The instructor is brilliant."

"Excellent course! The instructor is very knowledgeable..."

"Probably the best online course I've taken on a technical subject. The instructor's passion... is evident."

"Outstanding course! The instructor is truly passionate about CFD and it shows."

The material can be quite difficult.

"It is challenging, but incredibly rewarding."

"Yes, it's hard work..."

"It's a challenging subject, but this course makes it accessible."

"The material is dense and demanding..."

"Be ready for a challenge."

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 An Introduction to Computational Fluid Dynamics with these activities:

Review Calculus Fundamentals

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Solidify your understanding of calculus concepts, particularly derivatives and differential equations, as they are fundamental to understanding the numerical methods used in CFD.

Browse courses on Partial Derivatives

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Review differentiation and integration techniques.
Practice solving ordinary differential equations.
Work through example problems involving partial derivatives.

Review Linear Algebra Concepts

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Strengthen your knowledge of linear algebra, focusing on matrix operations and solving linear systems, as these are crucial for understanding the discretization of equations in CFD.

Browse courses on Eigenvalues

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Review matrix multiplication and inversion.
Practice solving systems of linear equations.
Understand eigenvalues and eigenvectors.

Read 'Computational Fluid Dynamics: The Basics with Applications'

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Supplement the course material with a widely used textbook that provides a comprehensive overview of CFD principles and applications.

View Fundamentals of Aerodynamics + Schaum's Outline... on Amazon

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Read the chapters related to finite difference methods.
Study the examples of CFD simulations.
Work through the end-of-chapter problems.

Four other activities

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Show all seven activities

Read 'Numerical Computation of Compressible Fluid Flows'

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Gain a deeper understanding of numerical methods for compressible fluid flows, complementing the course's introduction to CFD solvers.

View Putting Knowledge to Work on Amazon

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Read the chapters related to finite volume methods.
Study the examples of compressible flow simulations.
Compare the methods discussed with those presented in the course.

Implement a 1D Wave Equation Solver

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Reinforce your understanding of discretization and stability by implementing a simple solver for the 1D wave equation, a fundamental concept covered in the course.

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Choose a discretization scheme (e.g., finite difference).
Implement the scheme in Python or a similar language.
Test the solver with different initial conditions.
Analyze the stability of the solver.

Write a Blog Post on CFD Applications

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Deepen your understanding of CFD by researching and writing about its applications in various engineering fields, demonstrating the practical relevance of the course material.

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Research different applications of CFD.
Choose a specific application to focus on.
Write a blog post explaining the application and its benefits.
Include relevant images or simulations.

Simulate Flow in a Lid-Driven Cavity

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Apply the concepts learned in the course to simulate a classic CFD problem, the lid-driven cavity, which involves solving the Navier-Stokes equations.

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Set up the geometry and boundary conditions.
Choose a suitable numerical scheme.
Implement the solver and run the simulation.
Visualize and analyze the results.

Career center

Learners who complete An Introduction to Computational Fluid Dynamics will develop knowledge and skills that may be useful to these careers:

CFD Analyst

A Computational Fluid Dynamics Analyst specializes in simulating fluid flow using numerical methods. This course may serve as an excellent starting point for understanding the core principles behind CFD simulations. It helps build skills needed to analyze and interpret results. The course's coverage of topics like discretizing differential equations, assessing the stability of numerical schemes, and manipulating the Navier-Stokes equations will be essential tools for a CFD Analyst. You'll benefit from the course's exploration of models of varying fidelities and the practical experience gained from solving problems like lid-driven cavities and shock tubes using provided Python code.

See salaries and explore the career path for CFD Analyst

Research Scientist

Research scientists often use Computational Fluid Dynamics to investigate complex fluid phenomena. This course may offer a valuable introduction to the theoretical and practical aspects of CFD, helping you formulate and test hypotheses related to fluid behavior. The course's content on deriving and simplifying the Navier-Stokes equations, discretizing them using methods like MacCormack's scheme, and understanding error types will be crucial for conducting rigorous research. Furthermore, the focus on extending the provided solvers to handle variations of canonical problems directly supports the kind of innovative work that Research Scientists perform.

See salaries and explore the career path for Research Scientist

Mechanical Engineer

Mechanical engineers often work with fluid flow in various applications, making knowledge of Computational Fluid Dynamics highly valuable. This course may provide a foundational toolkit for understanding and simulating fluid behavior in systems like heat exchangers, pumps, and internal combustion engines. The course's emphasis on discretizing differential equations, understanding stability and accuracy, and deriving the Navier-Stokes equations will be directly applicable to your work as a Mechanical Engineer. You may find the course particularly useful given its discussion of explicit versus implicit methods and its insights into modified partial differential equations and error types.

See salaries and explore the career path for Mechanical Engineer

Aerospace Engineer

As an Aerospace Engineer, you need a strong understanding of fluid dynamics to design aircraft and spacecraft. This course, with its introduction to Computational Fluid Dynamics, may provide a solid foundation for modeling airflow around airfoils, analyzing the performance of propulsion systems, and simulating the behavior of spacecraft during atmospheric entry. The course's coverage of the Navier-Stokes equations, discretization methods, and error analysis directly applies to the challenges you will meet as an Aerospace Engineer. The lessons on using models of various fidelities and the included Python code for solving problems like shock-vortex interactions are especially relevant.

See salaries and explore the career path for Aerospace Engineer

Naval Architect

Naval Architects design and oversee the construction and repair of ships and other marine vessels. Computational Fluid Dynamics is a vital tool for optimizing hull designs and predicting vessel performance. This course may help you gain a foundational understanding of CFD principles applicable to simulating water flow around ships and optimizing their hydrodynamic efficiency. The course's focus on the Navier-Stokes equations, discretization methods, and error analysis will be directly relevant to your work as a Naval Architect. You'll find the exploration of models with varying fidelities particularly helpful.

See salaries and explore the career path for Naval Architect

Automotive Engineer

Automotive Engineers use Computational Fluid Dynamics to optimize vehicle aerodynamics, engine cooling, and fuel efficiency and this course may help provide a solid foundation in the principles of CFD. This introductory course will allow you to model airflow around vehicles, analyze heat transfer in engines, and simulate combustion processes. You should find the lessons on the Navier-Stokes equations, discretization methods, and error analysis particularly useful as an Automotive Engineer. Specifically, the course's coverage of models with different fidelities, along with the Python code for solving problems like shock-vortex interactions will be advantageous.

See salaries and explore the career path for Automotive Engineer

Hydraulic Engineer

Hydraulic Engineers design and analyze systems that involve the flow of fluids, especially water. This course may be useful because it provides an understanding of Computational Fluid Dynamics, which is applicable to modeling flow in rivers, pipelines, and hydraulic structures. The course’s instruction on discretizing differential equations, understanding stability and accuracy, and deriving the Navier-Stokes equations builds a strong base. As a Hydraulic Engineer, you should find particularly helpful the course's discussion of explicit versus implicit methods and its insights into modified partial differential equations and error types.

See salaries and explore the career path for Hydraulic Engineer

Environmental Engineer

Environmental Engineers use fluid dynamics to model the transport of pollutants in air and water. This course may provide the necessary knowledge to understand and simulate these complex processes. The course's emphasis on discretizing differential equations, understanding stability and accuracy, and deriving the Navier-Stokes equations may be directly applicable to your work as an Environmental Engineer. You may find the course particularly useful given its discussion of explicit versus implicit methods and its insights into modified partial differential equations and error types.

See salaries and explore the career path for Environmental Engineer

Meteorologist

Meteorologists study and forecast weather patterns, which are governed by fluid dynamics. This course may provide an understanding of Computational Fluid Dynamics, which is essential for modeling atmospheric flows. The course's coverage of the Navier-Stokes equations and discretization methods builds a solid foundation for your work as a Meteorologist. Lessons on using models of various fidelities and the Python code for solving problems like shock-vortex interactions may also be useful.

See salaries and explore the career path for Meteorologist

Chemical Engineer

Chemical Engineers often deal with fluid flow in reactors, pipelines, and other processing equipment. This course may provide a fundamental understanding of Computational Fluid Dynamics, which is useful for modeling and optimizing these systems. The course’s coverage of topics like discretizing differential equations, assessing the stability of numerical schemes, and manipulating the Navier-Stokes equations will be essential tools for your work as a Chemical Engineer. You may find the course particularly useful given its discussion of explicit versus implicit methods and its insights into modified partial differential equations and error types.

See salaries and explore the career path for Chemical Engineer

Acoustic Engineer

Acoustic Engineers analyze and control sound and vibration, often dealing with fluid-structure interactions. This course may familiarize you with Computational Fluid Dynamics, which is valuable for modeling sound propagation in fluids. The course's coverage of discretizing differential equations, understanding stability and accuracy, and deriving the Navier-Stokes equations are all relevant. Acoustic Engineers should also find the course's discussion of explicit versus implicit methods and its insights into modified partial differential equations and error types helpful.

See salaries and explore the career path for Acoustic Engineer

Biomedical Engineer

Biomedical Engineers apply engineering principles to solve medical problems, and fluid dynamics plays a crucial role in modeling blood flow and drug delivery. This course may introduce you to the fundamentals of Computational Fluid Dynamics, which helps in analyzing these processes. This course helps develop a toolkit that is useful for understanding fluid behavior in biological systems. The course's emphasis on discretizing differential equations, understanding stability and accuracy, and deriving the Navier-Stokes equations may be directly applicable to your work as a Biomedical Engineer.

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Software Developer

Software Developers creating simulation software can benefit from a deep understanding of the underlying scientific principles. This course may help you gain insights into the theory and implementation of Computational Fluid Dynamics algorithms. The course's coverage of topics like discretizing differential equations, assessing the stability of numerical schemes, and manipulating the Navier-Stokes equations will be essential tools to implement CFD solvers. You may find the course particularly useful given its discussion of explicit versus implicit methods and its insights into modified partial differential equations and error types.

See salaries and explore the career path for Software Developer

Data Scientist

Data Scientists with a background in fluid dynamics can apply their skills to analyze simulation data and extract meaningful insights. This course may provide you with the necessary context to understand the underlying physics and numerical methods used in Computational Fluid Dynamics. The course's coverage of topics like discretizing differential equations, assessing the stability of numerical schemes, and manipulating the Navier-Stokes equations will enable you to interpret simulation results accurately. You may find the course particularly useful given its discussion of explicit versus implicit methods and its insights into modified partial differential equations and error types.

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Teacher

Teachers in STEM fields can enrich their curriculum and provide students with a more comprehensive understanding of fluid dynamics by learning about computational methods. This course may help introduce you to the principles and applications of Computational Fluid Dynamics. The course's explanation of the Taylor series, discretization of differential equations, and the Navier-Stokes equations could be useful for preparing engaging and informative lessons. The examples of solving problems like lid-driven cavities and shock tubes using Python code can provide hands-on demonstrations for your students.

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An Introduction to Computational Fluid Dynamics

What's inside

Learning objectives

Syllabus

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Reviews summary

Rigorous introduction to computational fluid dynamics

Activities

Career center

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