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