LSU Mathematics Student Colloquium
The goal of the LSU Mathematics Student Colloquium is to give both undergraduate and graduate students the opportunity to hear and interact with speakers from across the country, providing information and perspective possibly relevant to their graduate and postgraduate careers.
Each invited speaker will spend several days at LSU, giving multiple talks and making himself or herself available to undergraduates.
Talks are not confined to the math department but open to everyone. Those majoring in related fields are encouraged to come.
We are a chartered LSU student organization (constitution and bylaws). We are munificently funded by the Student Government Programming, Support, and Initiatives Fund (PSIF), and the LSU Mathematics Department. We are grateful for the generous past funding made by grants from the National Science Foundation (a VIGRE grant) and the Board of Regents.
Wednesday April 23, 2025: Christopher Kees
Christopher is a CSRS Distinguished Professor in the Department of Civil and Environmental Engineering at Louisiana State University and is the LSU Coastal Ecosystem Design Studio’s Director. His research interests include fluid-structure interaction, multiphase fluid dynamics, sediment dynamics, water waves, coastal and riverine processes.
Student Colloquium ( Lockett 138; Wednesday, April 23, 3:30- 4:30 PM)
Title: Application of CutFEM to the modeling of coastal processes through vegetation
Abstract: Understanding the effects of sea level rise on coastal ecosystems involves complex solid materials, such as mixed sediments and vegetation. Physical flume and basin studies have long been used in coastal engineering to understand wave and current dynamics around such structures. Numerical flumes based on computational fluid dynamics and fluid-structure interaction have recently begun to augment physical models for design studies, particularly for engineered structures where established Arbitrary Lagrangian-Eulerian (ALE) methods based on boundary-conforming meshes and isoparametric or isogeoemtric finite element methods are effective. The rapid growth of lidar and photogrammetry techniques at large scales and computed tomography at small scales has introduced the possibility of constructing numerical experiments for the complex natural materials in coastal ecosystems. These methods tend to produce low-order geometric representations with uneven resolution, which are typically not appropriate for conforming mesh generation. To address this challenge, recent work [1] extended an existing ALE method to include embedded solid dynamics using a piecewise linear CutFEM approach [2]. The implementation is based on equivalent polynomials [3]. The approach retains the convergence properties of the CutFEM method while having a simple implementation within the existing twophase RANS model, which has been used frequently for numerical flume studies. This presentation will consider application and performance of the method for two critical coastal processes: wave interaction with vegetation and sediment dynamics.
REFERENCES
[1] C.E. Kees, J.H. Collins and A. Zhang, Simple, accurate, and efficient embedded finite element methods for fluid–solid interaction, Comput. Methods in Appl. Mech. Engrg., Vol. 389, 114404, 2022.
[2] A. Massing, B. Schott, and W. Wall, A stabilized Nitsche cut finite element method for the Oseen problem, Comput. Methods Appl. Mech. Engrg., Vol. 328, pp. 262–300, 2018.
[3] G. Ventura and E. Benvenuti, Equivalent polynomials for quadrature in Heaviside function enriched elements, Internat. J. Numer. Methods Engrg., Vol. 102 (3–4), pp. 688–710, 2015.
Gallery
See for photos of our previous student colloquiums.