151-0212-00L Advanced CFD Methods

Semester	Spring Semester 2022
Lecturers	P. Jenny
Periodicity	yearly recurring course
Language of instruction	English

Abstract	Fundamental and advanced numerical methods used in commercial and open-source CFD codes will be explained. The main focus is on numerical methods for conservation laws with discontinuities, which is relevant for trans- and hypersonic gas dynamics problems, but also CFD of incompressible flows, Direct Simulation Monte Carlo and the Lattice Boltzmann method are explained.
Learning objective	Knowing what's behind a state-of-the-art CFD code is not only important for developers, but also for users in order to choose the right methods and to achieve meaningful and accurate numerical results. Acquiring this knowledge is the main goal of this course. Established numerical methods to solve the incompressible and compressible Navier-Stokes equations are explained, whereas the focus lies on finite volume methods for compressible flow simulations. In that context, first the main theory and then numerical schemes related to hyperbolic conservation laws are explained, whereas not only examples from fluid mechanics, but also simpler, yet illustrative ones are considered (e.g. Burgers and traffic flow equations). In addition, two less commonly used yet powerful approaches, i.e., the Direct Simulation Monte Carlo (DSMC) and Lattice Boltzmann methods, are introduced. For most exercises a C++ code will have to be modified and applied.
Content	- Finite-difference vs. finite-element vs. finite-volume methods - Basic approach to simulate incompressible flows - Brief introduction to turbulence modeling - Theory and numerical methods for compressible flow simulations - Direct Simulation Monte Carlo (DSMC) - Lattice Boltzmann method
Lecture notes	Part of the course is based on the referenced books. In addition, the participants receive a manuscript and the slides.
Literature	"Computational Fluid Dynamics" by H. K. Versteeg and W. Malalasekera. "Finite Volume Methods for Hyperbolic Problems" by R. J. Leveque.
Prerequisites / Notice	Basic knowledge in - fluid dynamics - numerical mathematics - programming (programming language is not important, but C++ is of advantage)