Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science
Major
Mathematics
College
College of Arts and Sciences
Research Mentor
Amanda E. Diegel
Research Mentor's Department
Department of Mathematics and Statistics
Research Center
Center for Computational Sciences
Abstract
Poster created as part of the Center for Computational Sciences' Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science and presented at the 2024 Undergraduate Research Showcase.
We propose a numerical approximation method modeling two-phase flow (via the Cahn-Hilliard equation) that incorporates data to achieve long-time accuracy. The underlying numerical method utilizes the Galerkin finite element method for spatial discretization and a method known as continuous data assimilation to incorporate the known data. We demonstrate the method is long-time stable and long-time accurate provided enough data measurements are incorporated into the simulation, overcoming possibly inaccurate initial conditions. Numerical experiments illustrate the effectiveness of the method on a benchmark test problem. All computations are completed in MATLAB.
Presentation Date
Summer 8-2-2024
Keywords
computational mathematics, fluid flow
Recommended Citation
Graveman, Mary H. and Diegel, Amanda E., "Continuous Data Assimilation for Two-Phase Flow" (2024). Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science. 5.
https://scholarsjunction.msstate.edu/ccs-reu/5