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| AERO0030-1 | Computational fluid dynamics
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
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| Lecturer : | Vincent Terrapon |
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Language(s) of instruction :
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| English language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| This course is an introduction into computational fluid dynamics (CFD).
The material covered in this course follows very closely the required textbook. Additional details are added to some parts to complement the textbook.
The following topics are covered:
- Introduction (role of CFD, methodology, limitations)
- Basic equations of fluid mechanics (conservation laws, incompressibility, moving control volumes)
- Levels of approximations to the basic equations (Navier-Stokes equations, DNS, LES, RANS, boundary layer approximation, inviscid flows)
- Mathematical nature of the flow equations and boundary conditions (convection-diffusion equation, partial differential equation of second order, hyperbolic/ parabolic/ elliptic equations, conservation form of the equations, initial and boundary conditions)
- Finite difference method on structured grids (order of derivatives, order of accuracy, multi-dimensional space, non-uniform grids, centered and skewed stencils, implicit formulas)
- Finite volume and finite element methods (conservative discretization, general formulation, practical implementation, estimation of gradients, weak formulation, weighted residuals, Galerkin method)
- Structured and unstructured grid properties (non-uniform, body-fitted, multi-block, tetrahedral and hexahydral, hybrid, evaluation of cell areas and volumes, best practice)
- Consistency, stability and error analysis (definitions, von Neumann stability analysis, new schemes for convection, spectral analysis of numerical errors, numerical oscillations)
- General properties and high-resolution numerical schemes (two-level schemes, stability issues, generation of new schemes, monotonicity, Godunov's theorem, limiters)
- Time integration methods for space-discretized equations (matrix representation of operators, eigenvalue spectrum, Fourier modes, stability regions, implicit and explicit schemes, predictor-corrector schemes, ADI method)
- Iterative methods for the resolution of algebraic systems (point Jacobi and Gauss-Seidel, convergence analysis, overrelaxation, preconditioning, multigrid method)
- Numerical simulation of inviscid flows (influence of compressibility, discontinuities, space discretization, time integration, boundary conditions)
- Numerical solutions of viscous laminar flows (boundary conditions, grid, density-based methods, pressure correction methods, best practice)
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Learning outcomes of the course :
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| At the end of the course, the students should be able to:
- Apply the complete methodology of a CFD analysis
- Set up a simulation with an appropriate numerical method, correct boundary conditions, adequate initial conditions, and adequate parameter values
- Understand the basic options of a commercial or open source CFD software and their corresponding impact on the numerical solution
- Understand the close link between the physics, the equations and the numerical schemes
- Be able to assess a numerical scheme based on stability, consistency and accuracy considerations
- Know the major numerical schemes, their domain of applicability, and their advantages and shortcomings
- Differentiate between methods for incompressible and compressible flows
- Simulate a simple flow with a commercial or open source CFD code
- Critically assess CFD results
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Basic knowledge in fluid mechanics (conservation principles, Navier-Stokes equations, dimensional analysis, ...), in numerical analysis and in basic mathematics is required. |
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Planned learning activities and teaching methods :
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| The formal class hours focuses on the theory. Additionally, students are expected to regularly read the accompanying text book to consolidate this theory and gain a more in-depth understanding of some of the details omitted in class.
Homework problems are also distributed every week. Students are expected to work on them individually. These problem sets consist in solving analytical exercises or developing small programs in Matlab. They illustrate the concepts seen in class and help consolidate the material. They are also a very good preparation for the final exam. Homework problems are not graded. Weekly office hours are provided by the course assistant to answer questions about homework and theory.
Towards the end of the course, an applied exercise allows the students to familiarize themselves with a real CFD code. In particular, OpenFOAM is used and students have the opportunity to apply the full CFD analysis process to a simple flow case. |
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Mode of delivery (face-to-face ; distance-learning) :
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| The course is given in class. Exercises are done individually and independently by the students. A brief tutorial on OpenFOAM gives the required basis for the applied exercise. |
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Recommended or required readings :
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| A copy of some of the material presented in class is distributed electronically.
Required reading material:
- "Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics", C. Hirsch, 2nd ed., Butterworth-Heinemann
Recommended reading material and reference manuals:
- "Computational Methods for Fluid Dynamics", J.H. Ferziger & M. Peric, 3rd ed., Springer
- "Computational Fluid Dynamics", J. Anderson, 1st ed. McGraw-Hill
- "Fundamentals of Computational Fluid Dynamics", H. Lomax, T.H. Pulliam & D.W. Zingg, Springer
- "An introduction to Computational Fluid Dynamics: The Finite Volume Method", H.K. Versteeg & W. Malalasekera, 2nd ed., Pearson Education Limited
- "Fundamentals of Engineering Numerical Analysis", P. Moin, 2nd ed., Cambridge University Press
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Assessment methods and criteria :
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| The final grade for the course is based on a written exam. The exam questions are similar to the homework problem sets. |
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Work placement(s) :
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Organizational remarks :
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| The course is taught in English |
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Contacts :
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| Prof. V. E. Terrapon
Phone: +32(0)4 366 9268
Email: vincent.terrapon@ulg.ac.be
http://www.mtfc.ulg.ac.be/ |
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