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• Dr Irene Moulitsas

Object oriented programming (OOP) is the standard programming methodology used in nearly all fields of major software construction today, including engineering and science and C++ is one of the most heavily employed languages. This module aims to answer the question ‘what is OOP’ and to provide the student with the understanding and skills necessary to write well designed and robust OO programs in C++. Students will learn how to write C++ code that solves problems in the field of computational engineering, particularly focusing on techniques for constructing and solving linear systems and differential equations. Hands-on programming sessions and assignment series of exercises form an essential part of the course. The library support provided for writing C++ programs using a functional programming approach will also be covered.   

An introduction to the Python language is also provided.

• The OOP methodology and method, Classes, abstraction and encapsulation,
• Destructors and memory management, Function and operator overloading, Inheritance and aggregation, Polymorphism and virtual functions, Stream input and output,
• Templates, Exception handling, The C++ Standard Library and STL.

Functional programming in C++.

On successful completion of this module you should be able to:

• Apply the principles of the object oriented programming methodology - abstraction, encapsulation, inheritance and aggregation - when writing C++ programs,
• Design and create robust C++ programs of simple to moderate complexity given a suitable specification,
• Construct C++ programs to solve a range of numerical problems in computational engineering using both OO and functional based approaches, based on the Standard Template Library and other third-party class libraries,
• Design development environments and associated software engineering tools to assist in the construction of robust C++ programs,
• Evaluate existing C++ programs and assess their adherence to good OOP principles and practice.

• Dr Irene Moulitsas

The module aims to provide an understanding of a variety of computational methods for integration, solution of differential equations and solution of linear systems of equations.

The module explores numerical integration methods; the numerical solution of differential equations using finite difference approximations including formulation, accuracy and stability; matrices and types of linear systems, direct elimination methods, conditioning and stability of solutions, iterative methods for the solution of linear systems. Several of the studied numerical methods are implemented from scratch during the lab sessions, and the theoretical properties are then empirically studied and understood.

On successful completion of this module you should be able to:

• Formulate and assess numerical integration methods,
• Use appropriate techniques to formulate numerical solutions to differential equations,
• Evaluate properties of numerical methods, and choose the appropriate method to implement towards the solution of a given differential equation,
• Evaluate properties of systems of linear equations, and choose the appropriate method to implement towards the solution of a given system of linear equations,
• Assess the behaviour of the numerical methods and the computed numerical solutions.

To introduce basic concepts in the discretisation and numerical solution of the hyperbolic systems of partial differential equations describing the flow of compressible fluids.

• Mathematical properties of hyperbolic systems.
• Conservation Laws.
• Non-linearities and shock formation.
• WENO schemes.
• MUSCL schemes Introduction to the Riemann problem.
• Lax-Wendroff scheme.
• Introduction to Godunov's method.
• Flux vector splitting methods.
• Approximate Riemann solvers.
• Explicit and implicit time-stepping schemes.

On successful completion of this module you should be able to:

1. 1. Demonstrate a critical awareness of the mathematical properties of hyperbolic partial differential equations.
2. 2. Recognise the importance of non-linearities in the formation of shock waves.
3. 3. Distinguish the fundamental differences between monotone schemes, WENO schemes for hyperbolic systems.
4. 4. Judge the suitability of various Riemann solvers for various compressible flow problems.
5. 5. Create high-resolution shock capturing schemes for compressible flow problems.

Each computational investigation requires a CAD model from which numerical analyses can be performed. This is true for both CFD and FEA simulations, both of which students are exposed to during their studies on this MSc.

This module combines elements of CAD with an introduction to aerospace structures, focusing in particular on different components on the aircraft, as well as manufacturing philosophies which in turn inform the creation of parts (and CAD models).

You will learn how to build up various components of an aircraft using CATIA as the CAD software and will be capable of designing components themselves, based on drawings and technical documents, which they can then use to study numerically the behaviour of the component.

• Create drawings of a solid model using Catia.

• Create surface models using Catia.

• Create assemblies of different models in Catia.

• Create parametric models in Catia that can be updated through an external Excel sheet.

• Create FEA simulations of 2D shell and 3D solid parts in Catia.

• Perform optimisation of 2D and 3D geometries in Catia based on FEA results.

• Differentiate between fail-safe, safe-life and damage-tolerant design philosophies.

• Understand the constraints imposed by additional reserve factors on the structural components (limit and ultimate load factors).

• Understand the influence of fatigue on the life expectancy of a structure.

On successful completion of this module you should be able to:

1. 1. Create CAD models using commercial and industrial leading CAD software packages.
2. 2. Design various components found on aeroplanes from drawings and technical documents.
3. 3. Perform integrated Finite Element Analyses of structural components using Catia.
4. 4. Perform optimisation of structural components to minimise weight of the final assembly using global optimisation methods.
5. 5. Create parametric models that automatically update themselves based on external calculations.

Aerodynamics is of fundamental interest in computational aerospace science and engineering. It is taught as a standard undergraduate course on aerospace engineering courses. However, its complexity necessitates to approximate key aerodynamic coefficients through correlations and simplified theories; this is where this course comes into play.

Computational Aerodynamics does not rely on simplified theories but does employ Computational Fluid Dynamics (CFD) to solve the governing equations of fluid dynamics to replace these approximate theories and correlation-based tools, such as panel methods, lifting-line theory, potential flow-based methods, etc. This allows to provide estimates for efficiency factors (such as the Oswald efficiency factor) rather than relying on correlations, improved lift and drag values beyond the linear regime and these better predicted values can directly be used in flight mechanics models to calculate static and dynamic stability modes.

Aerodynamics for aerospace applications have further special modelling requirements which will be investigated and taught as part of this course. These include overset grid techniques to capture mesh motion of complex moving parts (e.g. flaps) and sliding mesh / frame motion to capture rotating objects (such as rotors, props, etc.).

Additionally, practical high-performance computing (HPC) aspects will be taught in the practical session of this module to provide students with the tools to run simulations on HPC systems.

• Review of key fluid mechanic and thermodynamic concepts.

• Review of key non-dimensional numbers.

• Calculate lift and drag polars and extracting different type of drags from simulations.

• Simulate viscous flow around aerodynamic bodies, including an extension to separated boundary layer flows.

• Extract key aerodynamic figures such as minimum drag and maximum lift over drag speed.

• Calculate centre of pressure and aerodynamic centre on aerofoils / wings / horizontal stabiliser and rudder and use extracted moments for static stability analysis.

• Perform CFD simulations for aerodynamic devices such as wings, aerofoil sections, flaps, etc. and use appropriate modelling strategy to capture the flow around these.

• Use shock-capturing schemes to resolve shock-waves for compressible flows, such as Riemann solvers.

• Apply mesh motion to simulate rotating domains (propellers, rotors, etc.).

• Automate the CFD calculation through scripting.

• Run automated CFD simulation on an HPC cluster environment.

On successful completion of this module you should be able to:

1. 1. Develop a suitable cleaned CAD geometry and create a suitable volume mesh using commercial pre-processing software packages.
2. 2. Perform aerodynamic simulations using Computational Fluid Dynamics (CFD) and appraise the different modelling techniques available to obtain aerodynamic coefficients, forces and moments and their computational cost / accuracy trade-off.
3. 3. Use high-performance computing (HPC) resources to perform complex aerodynamic flow calculations, which includes setting up automated simulations through scripting to be run on HPC systems.
4. 4. Calculate aerodynamic coefficients from raw CFD data and evaluate their differences to simplified aerodynamic correlations and mathematical theories from the literature.
5. 5. Develop a simulation environment that is able to capture laminar / turbulent and incompressible / compressible flows, including an understanding of shock-wave capturing schemes.

To understand the key features of mathematical modelling approaches and computational methods used for simulating flows relevant in aeronautical and aerospace applications.

• • Overview of the governing equations of fluid dynamics applicable to external flows including classical and advanced turbulence modelling approaches for aeronautical and aerospace applications.
• • CFD methods for low- and high-speed flows used for advanced aerospace applications.
• • CFD methods for digital wind tunnel applications.
• • State-of-the-art case studies and application examples.

On successful completion of this module you should be able to:

1. 1. Set up the governing equations of external fluid dynamics to simulate external flows in a digital wind tunnel.
2. 2. Collect data with a systematic approach and analyse computational results through numerical methods and models for turbulent flows used in aeronautical and aerospace applications.
3. 3. Evaluate the strength and limitations of computational methods used in the aerospace sector.
4. 4. Propose solutions in conjunction with the current efforts made by industry and academia for improving the state-of-the-art methods in the above applications.

The module is aimed at giving potential Finite Element users basic understanding of the background of the method. The objective is to introduce you to the terminology, basic numerical and mathematical aspects of the method. This should help you to avoid some of the more common and important user errors, many of which stem from a "black box" approach to this technique. Some basic guidelines are also given on how to approach the modelling of structures using the Finite Element Method.

• Introduction to Finite Element Methods (FEM) and applicability to different situations.

• Introduction to the Direct Stiffness (Displacement) Method.

• Development of Truss, Bar Element Equations in 2D and 3D.

• Development of Beam and Frame Element Equations (2D and 3D).

• Development of the Plane Stress element Equations (Constant and Linear Strain).

• Accuracy considerations: higher order elements, Isoparametric elements.

• The role of numerical integration and methods used in FE.

• Practical Considerations in Modelling; Interpreting Results.

On successful completion of this module you should be able to:

1. 1. Analyse and practice the theory of finite element models for structural and continuum elements.
2. 2. Design and solve mathematical finite element models.
3. 3. Interpret results of the FE simulations and analyse error levels.
4. 4. Create and solve mathematical finite element methods.
5. 5. Critically evaluate the constraints and implications imposed by the finite element method.

To introduce the concepts of validation and verification methods including the management of computational errors and uncertainties related to simulation of external flows for aeronautical and aerospace applications.

• • Mathematical foundations of uncertainty quantification methods and related theories including the definition of consistency, stability and convergence.
• • Taxonomies of numerical errors and uncertainties.
• • Principles of code verification for external flows.
• • Introduction to the method of manufactured solutions.
• • Principles of solution verification.
• • Principles of the generalized Richardson extrapolation including a method how to report numerical errors in a unified way based a proper grid convergence study.
• • Principles of mathematical model validation.
• • Statistical approaches to epistemic uncertainty.
• • Construction of validation and verification hierarchies.

On successful completion of this module you should be able to:

1. 1. Distinguish and analyse different classes of numerical errors and uncertainties for simulating flows used in aeronautical and aerospace applications.
2. 2. Evaluate the strength and weaknesses of computational approaches related to the potential sources of errors and uncertainties for aerospace applications.
3. 3. Critically evaluate the tools that are available for the quantification of error and uncertainty for simulating external flows used in aeronautical and aerospace applications.
4. 4. Set up reliable simulations through code verification and computational model validation.