An Introduction To Computational Fluid Dynamics

What you'll learn
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, expand and validate CFD solvers
Apply lessons learned to a handful of insightful applications like the shock tubes and lid-driven cavities
Requirements
Basic Calculus
Newton's Laws of Motion
Vector Calculus (Optional)
Programming (Optional)
No experience with CFD software assumed
Description
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 problemsAs 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
Overview
Section 1: Base Camp
Lecture 1 Course Overview
Lecture 2 A (Very) Brief History of CFD
Section 2: The Taylor Series Expansion
Lecture 3 Approximating Derivatives with the Taylor Series
Lecture 4 Approximating Derivatives with the Taylor Series
Section 3: Difference Equations
Lecture 5 Difference Equations
Lecture 6 Difference Equations
Lecture 7 Explicit vs Implicit Methods
Lecture 8 Roundoff Error and Von Neumann Stability
Lecture 9 Roundoff Error and Von Neumann Stability
Lecture 10 The Wave Equation
Lecture 11 The Wave Equation
Lecture 12 The Wave Equation
Section 4: The Navier-Stokes Equations
Lecture 13 Divergence
Lecture 14 Divergence
Lecture 15 Substantial Derivative
Lecture 16 Conservation of Mass
Lecture 17 Conservation of Momentum
Lecture 18 Conservation of Momentum
Lecture 19 Conservation of Energy
Lecture 20 Conservation of Energy
Lecture 21 The 'Fidelity Ladder'
Lecture 22 The 'Fidelity Ladder'
Section 5: Applications
Lecture 23 Potential Flow
Lecture 24 Potential Flow
Lecture 25 Potential Flow
Lecture 26 Streamfunction-Vorticity Formulation
Lecture 27 Streamfunction-Vorticity Formulation
Lecture 28 Streamfunction-Vorticity Formulation
Lecture 29 The Compressible Euler Equations
Lecture 30 The Compressible Euler Equations
Undergraduate students,Engineers looking to diversify their skills

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