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To introduce the foundations of fluid mechanics, various formulations of governing equations and their mathematical properties in order to establish a firm basis for other modules.

• Introduction to thermodynamics of gases and liquids
• Introduction to heat transfer
• Compressible flows
• Incompressible flows
• Dimensional analysis and similarity parameters
• Mathematics of governing equations, classification of PDEs
• Model equations for fluid dynamics
• Introduction to unstable and turbulent flows.

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

1. Distinguish and analyse the governing equations of fluid mechanics and heat transfer in various formulations for compressible and incompressible viscous and inviscid flows.
2. Estimate the impact of different physical phenomena based on dimensional analysis.
3. Examine mathematical properties of governing equations and be able to critically evaluate correct boundary/initial value problems for various flows.
4. Set up and analyse the systematic application of the model equations and problems used in CFD.
5. Distinguish and compare concepts of stability and turbulence.

To introduce the basics of numerical analysis and numerical methods for partial differential and algebraic equations, relevant to Computational Fluid Dynamics, and how to efficiently employ the latest technologies of high performance computing (HPC) for numerically solving these equations.

• Introduction to numerical analysis
• Discretisation approaches: finite difference, finite volume, finite element and spectral methods
• Numerical methods for algebraic equations/systems of equations
• Numerical schemes for hyperbolic, parabolic and elliptic systems and for fluid dynamics.
• Desktop versus distributed computing facilities
• Hardware and software aspects of HPC
• Parallel computing challenges and main issues
• Parallelisation approaches for distributed and shared memory systems. MPI & OPENMP
• Current CFD process with respect to partitioning and distributed computing and related bottlenecks
• Whole HPC product applications

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

To introduce the concepts of grid generation, including structured and unstructured approaches. To provide hands-on experience using commercial CAD and grid generation packages.

• Computer aided design interface with grid generation
• Geometry Modelling and Surface Grids
• Algebraic Mesh Generation
• Structured Meshes from Partial Differential Equations
• Automatic generation of Unstructured Meshes
• Multiblock Mesh Generation
• Unstructured grids by Delaunay Triangulation
• Mesh Adaptation on Unstructured Grids
• Unstructured Grids for Viscous Flows
• Grid generation tutorials with ANSYS Fluent Meshing and Pointwise

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

To provide an introduction into the use of visualisation, data mining, and interactive human-computer interfaces for the analysis and interpretation of CFD simulations. Visualisation can be a critical component in helping an engineer gain insight into the typically complex optimization problems that arise in design. Through the combination of visualisation and user interaction in computer tools, the engineer's insight can help guide the computer in the process of identifying better, more effective designs. Visualisation can also be combined with automated data mining techniques to improve optimization procedures.

To provide hands-on experience using both commercial and community developed visualisation packages.

To introduce the concepts of error and uncertainty and how they relate to the credible numerical solution of the partial differential equations encountered in computational fluid mechanics. You will be exposed to elements of wind tunnel testing and understand its strength and limitation as well as sources of differences between CFD and experimental results.

• Interpretation of data
• Graphical representation of data
• Parallel data visualisation
• Data mining, reduced order modelling, model identification and surrogate models
• Data fusion
• The right answer: consistency, stability and convergence revisited
• Taxonomies of error and uncertainty
• Principles of code verification
• Principles of solution verification
• Role of systematic iterative and space-time grid convergence studies
• Richardson extrapolation
• Principles of validation
• Construction of validation hierarchies
• Experimental techniques and their strength and limitation for comparative analysis against CFD data

On successful completion of this module a student should be able to:

1. Critically appraise alternative techniques for the visualisation and interpretation of CFD results.
2. Analyse commercial and community developed visualisation software packages to real CFD data.
3. Critically evaluate the use of limited simulation data when making engineering decisions.
4. Distinguish between error and uncertainty in computational simulations. Appraise the potential sources of error and uncertainty in computational simulations and wind tunnel testing.
5. Critically evaluate the tools that are available for the quantification of error and uncertainty in computational simulations and experimental studies, as well as be able to design/create and set-up credible computational simulations.

To introduce you to closure methods for the Navier-Stokes equations as applied to turbulent and transitional flows, and the classical physical modelling approximations required to achieve this. To introduce the advanced turbulence modelling approaches used in Computational Fluid Dynamics such as Large Eddy Simulations and Direct Numerical Simulations.

• Introduction to Reynolds Averaged Navier Stokes Modelling
• Zero, One and Two equation models
• Reynolds Stress Transport Schemes
• Low-Re Modelling
• Transition Modelling Extensions
• Best Practice Guidelines
• Overview of the basic equations used in LES, including filtered and unfiltered formulations
• Classical LES and sub-grid scale models
• Implicit LES (numerical and physical principles)
• Numerical and physical properties of DNS
• Applications and challenges for LES and DNS

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

1. Demonstrate a critical awareness of the basic principles of modelling approximations required to close RANS equations and Differentiate between different levels of closure and their limitations.
2. Appraise and Evaluate how modelling methods may be extended to transition prediction.
3. Critically compare between the different types of model available in current codes.
4. Demonstrate a critical awareness of the numerical and physical principles of LES and DNS in the simulation of transitional and turbulent flow simulations.
5. Critically evaluate the challenges in the implementation of LES and DNS in science and engineering.

• Dr Panagiotis Tsoutsanis

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:

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

​​To understand the state-of-the-art CFD methods used for computing incompressible flows in science and engineering.

• Overview of various formulations of the governing equations and numerical methods for incompressible flows (linear & high-resolution methods) .
• Solution approaches: pressure Poisson, projection (approximate and exact), artificial compressibility.
• Centred schemes.
• Introduction to simulation  and its application in the analysis of support problems for the delivery of value and the evaluation of associated risks.
• TVD and Riemann solvers for incompressible methods.
• Second and high-order methods (time and spatial discretise).