Course Details:
Instructor: Saverio Spagnolie
Time: TR 1-2:15pm
Room: Van Vleck B223
Course website: Piazza
Course Content:
We will begin by deriving the fundamental equations of continuum mechanics which describe the deformation and flow of a continuous medium. Our focus will be on viscous and complex fluid flows, including the Navier-Stokes equations as a special case. We will proceed to cover a wide variety of numerical techniques for studying physical problems, beginning with classical approaches like finite difference/volume methods and pseudo-spectral methods. Error analysis and accuracy/stability constraints will be discussed. Of particular interest will be numerical approaches for flows involving one or many moving interfaces/boundaries. Boundary integral methods, slender-body integral equations, and diffuse interface methods will be explored. Students will emerge prepared to compute the flows of complex (e.g. viscoelastic) and active fluids as well.
Each student will complete an independent course project, which will involve the development of a code and a numerical study of one or more real physical problems.
Prerequisites:
Students should have completed previous coursework in partial differential equations and numerical analysis.
