Abstract

Accurate simulation of incompressible steady-state fluid flow is critical for engineering applications where mass conservation, numerical stability, and geometric fidelity are essential. This thesis develops and analyzes a structure-preserving isogeometric framework for steady-state incompressible Navier"“Stokes simulations using truncated hierarchical B-splines (THB-splines). By leveraging divergence-conforming spline spaces designed to keep the fluid's divergence exactly zero based on the mathematical de Rham complex, this method ensures the fluid remains incompressible everywhere without needing extra stabilization techniques. The use of THB-splines allows the mesh to be refined locally in areas where the flow changes sharply. It still keeps the solution smooth and ensures the results are accurate. This thesis describes the mathematical formulations used to solve different types of fluid flow problems, including the L2 projection to keep the flow divergence-free, Stokes flow for simple cases, and the steady-state Navier-Stokes equations for more complex flows. While this thesis covers the L2 projection, Stokes flow, and Navier-Stokes equations its main contribution is solving the steady-state Navier-Stokes equations ensuring divergence-free results and the use of local refinement to improve accuracy and reduce computational costs. Tests on well known examples show that the method is accurate, keeps the flow divergence-free and captures important flow properties.

Degree

MS

College and Department

Ira A. Fulton College of Engineering; Civil and Environmental Engineering

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2025-07-31

Document Type

Thesis

Keywords

Steady Navier-Stokes, Incompressible fluid flow, Isogeometric analysis, B-splines, Structure-preserving splines, Hierarchical refinement, Computational fluid dynamics, Numerical simulation

Language

english

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