In this thesis, a combination of Isogeometric Analysis (IGA) and Finite Volume Method (FVM) on geometries parameterized by Non-Uniform Rational Basis Splines (NURBS) is explored with applications in fluid flow, heat transfer, and shape optimization. An IGA framework supplemented with FVM is created in MATLAB® to solve problems defined over single patch domains with mesh refinement by node insertion. Additionally, a second-order finite difference method is developed using non-orthogonal curvilinear coordinates and a numerical Jacobian of the NURBS geometry. The examples include fully developed laminar flow through ducts, potential flow around a tilted ellipse, transient heat conduction, linear advection-diffusion, and a basic shape optimization example using a particle swarm technique. The numerical results are compared among the methods and verified with available analytical solutions.
Library of Congress Subject Headings
Isogeometric analysis--Data processing; Finite volume method
Mechanical Engineering (MS)
Department, Program, or Center
Mechanical Engineering (KGCOE)
Pantaleón, Carlos, "Applications of Isogeometric Analysis Coupled with Finite Volume Method" (2014). Thesis. Rochester Institute of Technology. Accessed from
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