Mathematics for Engineers: The Capstone Course (Coursera)

Before enrolling, students should have already taken courses in matrix algebra, differential equations, vector calculus and numerical methods and be able to program in MATLAB.
The course contains 22 short video lectures and a full set of lecture notes. After each lecture there are problems to solve and at the end of the second and third weeks there is a substantial MATLAB programming assignment.
Course 5 of 5 in the Mathematics for Engineers Specialization.

What You Will Learn

• Computational Fluid Dynamics
• Scientific Computing

Syllabus

WEEK 1
Governing Equations
This week we learn the governing equations for the flow around a cylinder. We begin with the Navier-Stokes equations and the continuity equation, and derive a pair of coupled equations for the stream function and scalar vorticity. These equations are nondimensionalized and contain only a single dimensionless parameter called the Reynolds number. The governing equations are then simplified using log-polar coordinates.

WEEK 2
Steady Flows
In this week, we formulate the computational fluid dynamics problem of the steady flow around a cylinder. We introduce the finite difference method and derive iteration equations. Boundary conditions are derived and the outline of a MATLAB program is discussed. Students will write a program to compute the stream function at a Reynolds number of ten.

WEEK 3
Unsteady Flows
In this week, we formulate the computational fluid dynamics problem of the unsteady flow around a cylinder. We introduce periodic boundary conditions in the polar angle and show how to solve for the stream function using matrix methods. The solution for the scalar vorticity will use a MATLAB ode integrator. Students will write code to compute the time-dependent scalar vorticity at a Reynolds number of sixty.