Finite Element Methods for Fluid Dynamics

Uitgebreide vaknaam	Finite Element Methods for Fluid Dynamics
Leerdoelen	At the end of the course, the student is able to: 1) implement a finite element solver of the incompressible Navier-Stokes equations in arbitrary geometries 2) asses the issues arising in fluid dynamic simulations and propose solutions according the theory 3) explain conditions to ensure solvability of the discrete problem 4) apply stability analysis to continuous and discretized equations in fluid dynamics
Omschrijving	The goal of this course is to learn how to implement finite element approximations of flow problems and to analyze the quality of the numerical results in view of the theory. We will achieve this goal by dealing with equations of increasing complexity. First, we will solve stationary problems: Projections of functions -> Laplace->Advection-Diffusion->Stokes. Then, we will solve transient problems: Heat->Stokes->Navier-Stokes. Practical works in Python (using the finite element library FEniCS) will allow exercising and verifying the theory in practical examples. The course is therefore well adapted for students with knowledge of numerical fluid mechanics using other discretization methods, as well as students who want to learn (more) about finite elements methods in general and who are also interested in applications behind flows.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Practisch werk (PRC) (Practical work will be based on assisted sessions and non-assisted personal work.)
Toetsvorm	Practisch werk (PR), Schriftelijk tentamen (WE) (For passing, WE >= 5.5 and each PR >= 5.5. The final grade is then F = 0.3 WE + 0.7 PR. The practicals are mandatory.)
Vaksoort	master
Coördinator	dr. C.A. Bertoglio
Docent(en)	dr. C.A. Bertoglio
Entreevoorwaarden	Numerical methods as taught in Numerical Mathematics 1 (WINM1-07). Knowledge of partial differential equations, either acquired in a theoretical context (e.g. WIPD-07) or applied context (like in a fluid mechanics course). Experience in programming in Python, Matlab, Octave, or any similar environment.
Opmerkingen	Students who took the course Modeling of Fluid Flow in 2017-2018 are not allowed to take the course Finite Element Methods for Fluid Dynamics due to a similarity in the content. This course was registered last year with course code WMMA18001
Opgenomen in	Opleiding Jaar Periode Type MSc Applied Mathematics: Computational Mathematics  ( MSc Applied Mathematics: Computational Mathematics ) - semester II a keuzegroep MSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester II a MSc Mechanical Engineering: Advanced Instrumentation  (Electives ) 1 semester II a keuze MSc Mechanical Engineering: Materials for Mechanical Engineering  (Electives ) 1 semester II a keuze MSc Mechanical Engineering: Process Design for Energy Systems  (Electives ) 1 semester II a keuze MSc Mechanical Engineering: Smart Factories  (Electives ) 1 semester II a keuze