UROP Project

Asymptotically preserving numerical method for incompressible or compressible multiphase flows

fluid mechanics, deforming boundary problems, high performance computing

Research Mentor: Mark Sussman,
Department, College, Affiliation: Mathematics, Arts and Sciences
Contact Email: msussman@fsu.edu
Research Assistant Supervisor (if different from mentor):
Research Assistant Supervisor Email:
Faculty Collaborators:
Faculty Collaborators Email:

Looking for Research Assistants: Yes
Number of Research Assistants: 1
Relevant Majors: engineering, department of scientific computing, math, physics, or computer science
Project Location: On FSU Main Campus
Research Assistant Transportation Required:
Remote or In-person: Partially Remote
Approximate Weekly Hours: 10, Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Roundtable Times and Zoom Link:
Not participating in the roundtable

Project Description

An "asymptotically preserving" numerical method for fluid mechanics is a method that works for both incompressible flows and compressible flows with the "relaxed" requirement that max|u|\Delta t <= \Delta x. I say "relaxed" because the standard requirement is max (|u|+c)\Delta t<=\Delta x. "c" is the sound speed of the fluid.

We have recently developed an improved "asymptotically preserving" method that, so far, works well. But the method needs to be tested more! Ideally, if a student can prove analytically that the method works for all cases, and then that student will win the millenial prize!

The student' role will be to test the new "asymptotically preserving" method on a class of "Riemann" problems. Also, it might be illuminating if the student codes up his/her own version of the algorithm.

Research Tasks: Literature review: what has been proved regarding convergence of numerical methods for fluid mechanics?
data collection: as stated above "The student' role will be to test the new "asymptotically preserving" method on a class of "Riemann" problems. Also, it might be illuminating if the student codes up his/her own version of the algorithm. "


Skills that research assistant(s) may need: student needs to know how to computer program or is seriously interested in learning. Also, student should have knowledge of partial differential equations (or is concurrently taking the class).