This MSc thesis is centred around better capturing the physics of Navier-Stokes flow problems with the following two CFD methods that preserve integral invariants. A recent 2D mass, kinetic energy, enstrophy and total vorticity conserving (MEEVC) method is the cornerstone of this work. It was constructed with mimetic concepts in mind and its favourable properties were a reason to use it as inspiration for developing a novel 3D mass, kinetic energy and helicity conserving (MEHC) method. This method has a separate equation for the evolution of helical density in its formulation, a feature which is possibly unique in CFD.

With the ever-growing semi-conductor market the need for more advanced and faster chips rises. To keep the steady trend of Moore’s law going, which states that the transistors on a microchip double every two years, the micro chip manufacturing processes have to become more and more precise. The current state of the art Extreme Ultra Violet Light (EUV) lithography systems produced by ASML can manufacture chips with precision of printing up to 2 nanometers. At these scales even the smallest particles can affect the production processes of chips.
To circumvent the interference of molecules or debris in lithography machines flow simulations are performed to determine how to design flows to clear out these contaminants. Since most areas of the EUV machine are under rarefied gas conditions, normal continuum approaches fall short to predict the flow conditions. For rarefied flows the Direct Simulations Monte Carlo (DSMC) solver called SPARTA (Stochastic Parallel Rarefied-gas Time-accurate Analyzer) can be used. There are more methods to model rarefied gas flows, however the SPARTA program is open-source, adaptable and scales well on parallel computing systems. The last one of the three implies that simulations can be accelerated on High Performance Computing (HPC) clusters. Although the parallel computing accelerates the process, the simulations remain expensive. For instance, the 3D simulation of a scanner section contains 1 billion particles and needs a simulation power of 2000 cores for upwards of 45-80 hours of simulation time.
Consequently, it is necessary to continually develop methods to reduce computational costs for gas flow simulations. In particular cases where the contaminant concentration is so low that the effect of contaminants on the carrier gas can be neglected. In such cases the effects of a flow field on the contaminants can be passively modelled, and this method was dubbed the name Passive Scalar Approach (PSA). In other words, there are no carrier gas particles to actively participate in the collisions. The objective of this thesis is to reduce computational costs of a rarefied gas simulation with DSMC method on SPARTA by means of the PSA method.
First, the PSA capabilities were added to the SPARTA code. The PSA was implemented such that the steady-state background flow for a specific flow domain is first generated. Once this background flow field is imported into SPARTA, the contaminants can be loaded on top of the background flow with various concentrations, distributions, and at various locations within the simulation domain. The interactions between the contaminant and the background flow within every simulation cell is determined by the stream velocity of the background file, temperature and the velocity of the contaminant particles, using a Variable Soft Sphere (VSS) collision model. No active carrier gas particles need to be loaded into the memory of the solver.
Next, the PSA method was compared against a DSMC simulation with active carrier gas particles (referred to as a “full DSMC simulation”) for two cases: 1. Brownian motion in a box with homogenous carrier concentration, and 2. contaminant injection in a Poiseuille flow. Both cases showed similar diffusion rates indicating that the PSA models the full DSMC. In the Poiseuille flow case, an additional molecular scattering analysis showed similar scattering behaviour to the full DSMC collision model on a microscopic level. A significant decrease in computational costs was noted for the PSA in both cases. The findings in this thesis describe the promising results of implementing the PSA to model rarefied aerodynamic behaviour in SPARTA, with significant computational gains.

This study proposes a novel approach, developing and analyzing a higher-order, structure-preserving discretization method for inviscid barotropic flows from a Lagrangian perspective. The discretization encodes flow variables as discrete differential forms on a space-time mesh, using principles from differential geometry and algebraic topology. Unlike standard Lagrangian methods, which are prone to mesh distortion, this framework computes fluid deformations in a reference configuration and systematically maps them to the physical domain. This structure-preserving design ensures that fundamental conservation laws for mass, momentum, and energy hold up to machine precision. It also efficiently handles low-Mach number flows without specialized fixes for stiff pressure waves. Numerical experiments on expansion and compression flows confirm the discretization’s accuracy, stability, and conservation properties. The formulation naturally couples with structural solvers, enabling fluid-structure interaction and other multi-physics applications. By uniting spectral accuracy with a geometry-aware design, this approach serves as a first step toward a complete Lagrangian spectral element solver.

The rapid advancement of science and technology is driven by the goal of improving life on Earth while maintaining environmental responsibility. This progress is evident across numerous fields. In wind energy, the continuous development of new wind turbine designs and innovative wind farm configurations is crucial for accelerating the energy transition. The aerospace industry constantly introduces advanced airplane and helicopter designs to improve performance and efficiency. Urban planning increasingly relies on detailed analysis to optimize airflow within cities, addressing environmental and health concerns. These are just a few examples where innovation is driven by the need to enhance performance and sustainability.

A common requirement across these diverse fields is the need for an in-depth understanding of aerodynamics. Accurate aerodynamic analysis is essential for enhancing design, efficiency, and effectiveness. However, the fast-paced nature of modern advancements limits reliance on experimental methods alone, as these can be time-consuming, costly, and impractical for all possible configurations. Consequently, combining experimental and computational studies becomes crucial.

This is where Computational Fluid Dynamics (CFD) comes into play. The development of efficient and accurate CFD tools has become essential in scientists' and engineers' hands to explore aerodynamics quickly and understand the physics of the flows. This fact has driven the present research. The primary goal of this dissertation is the development of a computational tool that is both accurate and efficient for exploring external aerodynamics simulations.

The main approaches in CFD today are the Eulerian and Lagrangian approaches, each comprising a family of methods. Eulerian methods, like the Finite Volume Method (FVM) and Finite Element Method (FEM), have been extensively used in exploring external aerodynamics, with their greatest advantage being accuracy in capturing the boundary layers. However, due to the diffusive nature of these methods, artificial diffusion is introduced into the flow, damping the vortex structures, which are crucial in many applications driven by strong body-vortex interactions. Moreover, the study of multibody objects often requires special treatments, especially for mesh generation, making the simulations extremely costly.

On the other hand, Lagrangian methods, like the Vortex Particle Method (VPM), are excellent for studying flows with a high presence of vortices, as they can preserve the vortex structures without damping them. Additionally, the particles participating in the flow are self-adaptive, satisfy the far-field boundary conditions automatically, and allow for easy implementation of multiple bodies into the simulation. However, resolving the boundary layer is very challenging and often very costly due to the inability to use anisotropic elements, making them less ideal for predicting aerodynamic forces.

Lagrangian solvers have become very popular in the last two to three decades, primarily due to the significant advancements in computer hardware, especially GPUs, which enable very fast calculations. This has encouraged engineers to explore ways to leverage this advantage in CFD, leading to the development of hybrid solvers that couple Eulerian and Lagrangian solvers. In this coupled approach, Eulerian solvers can be applied near the solid body to accurately and efficiently resolve the boundary layer region, while Lagrangian solvers preserve the vortex structures further from the body.

Building on this approach, this dissertation introduces a hybrid Eulerian-Lagrangian solver, named VPMFoam, developed to combine the strengths of both methods while minimizing their limitations. This is achieved by integrating OpenFOAM, a widely used open-source CFD software, with a Lagrangian VPM. The primary goal is to create an accurate tool focused on external aerodynamics that can efficiently handle cases with strong body-vortex interactions and multibody scenarios while maintaining a lower computational cost compared to pure Eulerian solvers. OpenFOAM was chosen primarily for its open-source flexibility and its extensive user base in academia and industry, offering broad access to this tool.

The solver's development focuses on a 2D version, with validation conducted through a step-by-step approach, starting with simple cases that exclude solid bodies. Once the successful coupling of the two solvers is verified, validation proceeds with cases involving solid bodies, such as flow around a cylinder. In these cases, the solver accurately predicts fluid flow and aerodynamic coefficients, showing strong agreement with established Eulerian solvers and effectively preserving the vorticity field in the wake. Further validations address dynamic mesh motions and multibody applications.

Following validation, the solver is applied to more realistic scenarios, including the static and dynamic stall of an airfoil and the simulation of hybrid Vertical Axis Wind Turbines using actuator models. A performance analysis of the code’s efficiency is also presented, highlighting the solver’s capability to conduct fast and accurate simulations.

By effectively combining the strengths of both Eulerian and Lagrangian approaches, VPMFoam addresses key challenges in aerodynamic analysis, particularly in cases with strong body-vortex interactions, and lays a strong foundation for further applications, including potential 3D extensions. This makes VPMFoam a valuable asset for applications requiring both high fidelity and computational efficiency.

This thesis investigates the flow and heat transport phenomena in a pipe and Pressurized Water Reactor (PWR) rod bundle geometries using high-fidelity Direct Numerical Simulation (DNS). These geometries are essential for nuclear reactor systems, where efficient heat transfer and stable flow patterns are vital to ensure operational safety, reliability, and performance. The study focuses on evaluating the limitations of traditional thermal-hydraulic modeling approaches and advancing the understanding of flow physics in complex geometries.
Since Computational Fluid Dynamics (CFD) simulations are computationally expensive, system codes such as RELAP5, TRACER, and SPECTRA (developed by NRG) are widely used in reactor safety and design analysis. These codes rely on conventional pipe flow correlations to approximate thermal-hydraulic behavior, which are not representative of the intricate flow patterns observed in rod bundle arrangements. Such geometries are characterized by secondary vortices, gap street vortices, and the coupling of these vortices across multiple planes, forming a complex rod bundle vortex network. This study addresses these challenges by comparing the flow and thermal characteristics of pipe and subchannel geometries to evaluate the validity and limitations of pipe-based correlations.
To identify the subchannel geometry that best represents a rod bundle arrangement, square and 2×2 subchannel configurations were selected for detailed investigation. These geometries were modeled with a pitch-to-diameter (P/D) ratio of 1.3263, typical of PWR fuel assemblies, and simulated at a Bulk Reynolds number (Reb) of 5300. The square subchannel geometry represents a simplified cross-sectional domain, while the 2×2 subchannel configuration captures inter-subchannel interactions and the enhanced coupling effects seen in rod bundles. Using the Nek5000 spectral element solver, the simulations employed advanced numerical techniques, including spatial-temporal averaging through flow-through time (FTTs) metrics and further spatial averaging over unit cells, to achieve statistically converged results. Rigorous validation of pipe configuration with reference data ensured the accuracy of the computational framework.
The results highlight significant differences in turbulence structures and heat transfer performance between the pipe, square subchannel, and 2×2 subchannel configurations. While pipe correlations provide a baseline for comparison, they fail to capture the complex flow interactions observed in rod bundles. The 2×2 subchannel geometry emerges as a more accurate representation of rod bundle dynamics due to its ability to simulate enhanced inter-subchannel mixing and vortex coupling. These findings emphasize the importance of geometry-specific modeling in accurately predicting thermal-hydraulic behavior in nuclear reactors.
This work bridges the gap between simplified system codes and detailed physics-based modeling of rod bundle flows. The insights gained from this study provide a foundation for improving thermal-hydraulic predictions and advancing the design and safety of nuclear reactor systems. Future research will extend these findings to explore higher Reynolds numbers, diverse Prandtl numbers, wall effects, and alternative rod bundle configurations, further contributing to the development of advanced engineering tools for nuclear applications.

As the automotive industry increasingly shifts toward electrification, reducing vehicle drag becomes crucial for enhancing battery range and meeting consumer expectations. Additionally, recent European regulations require tire and car manufacturers to provide reliable drag data. A significant factor influencing vehicle drag is the highly turbulent wake generated by rotating tires. Accurate correlation between wind tunnel experiments and numerical simulations is essential, yet discrepancies often arise due to the dynamic behavior and technical challenges in measuring tire deformation, leading to inconsistencies between tire deformations observed in wind tunnels and those modelled in simulations.

This Master’s Thesis investigates the aerodynamic impact of realistic tire deformation parameters—specifically, bulge and contact patch deformations—using Computational Fluid Dynamics (CFD) simulations conducted with PowerFLOW. The deformation parameter tests are carried out in a standalone tire setup, which is validated from previous work by Dassault Systèmes and experimental results. To further assess the impact of these deformations on vehicle drag, the tests were repeated using the DrivAer model, an IP free model provided by the Technical University of Munich. Given the complexity of the flow features in a tire wake, the analysis of the results consisted of two different approaches: a statistical approach based on Principal Component Analysis (PCA), and a vortex behaviour and wake development analysis, including a vortex tracking algorithm based on the Gamma 2-Criterion and single-link hierarchical clustering.

The results identify the most influential deformation parameters based on their impact on the drag coefficient and the wake behaviour changes. Two primary wake development behaviours were identified: wake contraction and wake expansion. An analysis of the transient flow showed how these two trends resulted from changes in the unsteady behaviour introduced by certain deformation parameters. The relevance of these wake development changes was portrayed by the impact of certain deformations on the full vehicle drag as a result of
complex wake interactions.