A Conservative Numerical Scheme for the Multilayer Shallow Water Equations

Author

Evan ButterworthFollow

Date of Award

5-2022

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

School of Mathematical and Statistical Sciences

Committee Chair/Advisor

Qingshan Chen

Committee Member

Lea Jenkins

Committee Member

Vince Ervin

Abstract

An energy-conserving numerical scheme is developed for the multilayer shallow water equations (SWE’s). The scheme is derived through the Hamiltonian formulation of the inviscid shallow water flows related to the vorticity-divergence variables. Through the employment of the skew-symmetric Poisson bracket, the continuous system for the multilayer SWE’s is shown to preserve an infinite number of quantities, most notably the energy and enstrophy. An energy-preserving numerical scheme is then developed through the careful discretization of the Hamiltonian and the Poisson bracket, ensuring the skew-symmetry of the latter. This serves as the groundwork for developing additional schemes that preserve other conservation properties of interest for the multilayer case.

Recommended Citation

Butterworth, Evan, "A Conservative Numerical Scheme for the Multilayer Shallow Water Equations" (2022). All Theses. 4077.
https://tigerprints.clemson.edu/all_theses/4077

Author ORCID Identifier

https://orcid.org/0000-0002-6153-2938