Structure Preserving Isogeometric Analysis for Computational Fluid Dynamics

Structure Preserving Isogeometric Analysis for Computational Fluid Dynamics

Janssen, S.R.

Gerritsma, M.I. (mentor)
Möller, M. (mentor)

Aerospace Engineering

Aerodynamics, Wind Energy, Flight Performance and Propulsion (AWEP)

M.Sc. Aerospace Engineering

2016-11-18

Double degree. Supervision of the thesis also at: Faculty Applied Mathematics, Department Numerical Analysis, Programme M.Sc. Applied Mathematics. Structure-preserving discretization techniques preserve fundamental structure of operators and operands found in partial differential equations. Classical discretization techniques sometimes neglect these structures, and as a result, fail to simulate the desired physica behavior. In this thesis the existing structure-preserving framework for elliptic partial differential equations is applied to isogeometric analysis. De Rham conforming B-splines are derived that conserve the topological structure of the derivative operator in the discrete setting. This framework is expanded to be able to discretize hyperbolic partial differential equations, which is applied to derive an energy-preserving discretization for the incompressible Euler equations.

structure-preserving
isogeometric analysis
B-splines
computational fluid dynamics
discretization
differential geometry
algebraic topology
incompressible
Euler equations
De Rham cohomology
exterior derivative
interior product
energy-preserving
mimetic

http://resolver.tudelft.nl/uuid:2f4975f9-17b0-4fd5-949e-8d551e5d4dfe

Student theses

master thesis

(c) 2016 Janssen, S.R.