Intermediate Fluid Mechanics

The class combines classical analysis and numerical methods in fluid mechanics. Topics include derivation, scaling, and approximations to the Navier‐Stokes equations (conservation of fluid mass and momentum), advective and diffusive transport of momentum and scalars, turbulence, and numerical solution of hyberbolic, parabolic, and elliptic partial differential equations.  

The class focuses on problems in environmental fluid mechanics, e.g. open channel and oscillatory flow, wave theory, density‐driven circulation, and turbulent mixing.  Because intermediate and advanced classes in fluid mechanics involve an intensive study of Navier‐Stokes equations, numerical modeling is an indispensable part of the curriculum: The Navier‐Stokes equations are unsolved analytically, yet amenable to numerical simulation.  

Students use Matlab to develop numerical solutions to ordinary and partial differential equations originating from problems in fluid dynamics.  By the end of the course, students develop the computational skills necessary to write their own CFD models in idealized configurations and evaluate the performance of commercial CFD codes used in industry.

Example of a programming assignment: A CFD code for a lid-driven cavity problem

 A lid-driven cavity flow at Reynolds number (Re) = 1000.  Left panel: velocity and vorticity field; Right panel: colored tracer particles.

A lid-driven cavity flow at Reynolds number (Re) = 1000.  Left panel: velocity and vorticity field; Right panel: colored tracer particles.

 A lid-driven cavity flow at Re = 10000. At a higher Reynolds number, the flow forms smaller-scale eddies.

A lid-driven cavity flow at Re = 10000. At a higher Reynolds number, the flow forms smaller-scale eddies.