Mimetic Discretization of the High Frequency Helmholtz Equation using Hermite Interpolating Polynomials

Numerical modelling of high frequency waves is a complex and challenging area. Although the underlying equation seems simple, −∆φ − k2φ = f, the numerical challenges are not. This time harmonic wave equation is known as the Helmholtz equation. The main challenge to be studied is the pollution error, which is the difference between the actual and...

Energy-conserving spectral element schemes based on Lagrangian dynamics: Investigating discrete energy conservation

Physical systems in the continuous domain are often solved using computer-aided software because of their complexity. Preserving the physical quantities from the continuous domain in the discrete domain is therefore of utmost importance. There is however a broad range of techniques that can accomplish the translation between the continuous and...

Effect of atmospheric boundary layer inflow and wind yaw angle on the aerodynamics of heavy duty vehicles and attached boat-tails

Greenhouse gas emissions have globally increased temperatures and have led to global warming. A major part of these greenhouse gas emissions is emitted by motor vehicles in Europe. With an aim to limit global temperature increase by targeting emissions from heavy duty vehicles (HDV) which travel long-haul international journeys, this thesis aims...

Tip vortex modelling for cavitation noise applications: A verification and validation study in ReFRESCO

Cavitating tip vortices of marine propellers are the main contributors to underwater radiated ship noise due to their dynamic behavior and broadband sound spectrum. Experimentally, it is challenging to get a detailed insight into the vortex structure which makes it difficult to understand the noise generating mechanisms. Although Computational...

Jensen-Gaussian wake model extension considering the Atmospheric Boundary Layer effects for the Wind Farm Layout Optimization

To increase the total wind farm power output, the wind farm layout needs to be optimized. The power output of a wind turbine depends on the incoming velocity, while the velocity is influenced by the wake of the upstream wind turbines. Wind Farm Layout Optimization (WFLO) problems makes use of the so called low fidelity wake models, which...

Advancing the Mimetic Spectral Element Method: Towards Continuum Mechanics Applications

Mimetic discretisation techniques are a growing field in computational physics research. Among these techniques, the recently developed mimetic spectral element method allows for exact discretisation of metric independent relations. This has been proven numerically in various mixed formulations, for instance the mixed velocity-vorticity-pressure...

Identiffcation of Momentum Forcing Required to Reduce Base-Model Errors Using Full-Field Inversion

Reynolds Averaged Navier-Stokes turbulence models have been widely used in many industrial applications because of their lower computational cost compared to other simulation approaches such as DNS and LES. This is a consequence of considering mean-ow quantities achieved by the time-averaging process. However, the time-averaging introduces the...

A Finite Element Method with Special Edge-Polynomials for Advection Problems

The field of Computational Fluid Dynamics (CFD) is constantly finding new ways to improve simulation results. One of the large challenges in CFD, is advection. Advection dominated flows are governed by hyperbolic equations, which pose severe stability issues. Stabilized methods usually add significant numerical diffusion, which alters the...

Path-consistent schemes for interacting boundary layers: A discontinuous Galerkin approach

This study is aimed at modelling of the unsteady interacting boundary layer around wind turbine rotor blades. It is shown that nonconservative mechanisms are present in this system, affecting the definition and approximation of solutions to the problem. The objective is to overcome the inconsistency of classical (dissipative) schemes, and find a...

Variational Germano Optimization of Arbitrary Unresolved-Scale Models

This thesis demonstrated how the Newton and BFGS algorithm could be used to solve the standard VGM relations and least-squares formulation respectively, for arbitrary forms of the _ parameter, including nonlinear _ s, appearing in the VMM. The proposed procedure were also shown to be able to handle arbitrary projectors that are compatible with...

Slow and Fast Hydrogen De agration: A validation study

Amidst the growing demand for energy, many nations are considering the expanded role of nuclear power in their energy portfolios. However, in case of severe accidents, large amounts of hydrogen gas can be released in the nuclear containment. Hydrogen-air mixture forms a very ammable gas which on subsequent ignition can lead to ame propagation in...

Energy, vorticity and enstrophy conserving mimetic spectral method for the Euler equation

The behaviour of an inviscid, constant density fluid on which no body forces act, may be modelled by the two-dimensional incompressible Euler equations, a non-linear system of partial differential equations. If a fluid whose behaviour is described by these equations, is confined to a space where no fluid flows in or out, the kinetic energy,...

Mimetic Discretizations with B-Splines: On the Construction of a Discrete Hodge Star Operator

This thesis introduces a higher-order numerical method for elliptic boundary value problems. The discretization method belongs to the class of mimetic discretizations, which translate as many of properties of the continuous problem to the discrete system, aiming to improve accuracy and reliability. The novelty lies in the application of B...

An Adjoint Approach to Error Estimation for Mimetic Spectral Element Method

Mimetic Mesh Refinement: A mortar element approach

This thesis aims to introduce mesh refinement into the Mimetic Spectral Element Method (MSEM). The concept of mimetic discretizations is to mimic the properties of continuous Partial Differential Equations (PDEs) discretely. In many discretization methods information is lost in the actual discretization step which is detrimental to the physical...

A Geometric Approach Towards Momentum Conservation: Using design tools based on finite difference and integral methods

The equations governing fluid-flow are a set of partial differential equations, as is the case for a host of other continuous field problems. Analytical solutions to these problems are not always available and computers are unable to handle continuous representations of variables. This makes a finite-dimensional projection mandatory for all...

Finite Element Methods with exact geometry representation: IsoGeometric Analysis, NURBS Enhanced Finite Element Method and AnisoGeometric Analysis

Traditionally, geometry has been represented differently in the field of Computer Aided Design (CAD) and Finite Element Analysis (FEA). This means that the CAD geometry, which can be seen as exact, must be converted to an Analysis Suitable Geometry (ASG) for input in a FEA program. A cumbersome and time consuming process, more commonly known as...

IsoGeometric Mimetic Methods: Applied geometry in CFD

In this thesis I present a novel discretization procedure which combines two relatively new technologies for solving partial di_erential equations (PDE's): IsoGeometric Analysis (IGA) is a new paradigm which provides an exact geometry description and tight integration of Computer Aided Design (CAD) and Finite Element Analysis (FEA) by using the...