**June 29, 2016 at 10:00**

**Speaker(s):**
** Johan JANSSON, Johan HOFFMAN**

**Center(s): **BCAM and KTH, KTH and BCAM

**Summer School on Advanced Computation in Fluid Mechanics - "New Theory of Flight"**
**June 29 - July 1, 2016**
** BCAM - Basque Center for Applied Mathematics, Mazarredo 14, Bilbao, Basque Country, Spain**
This is an advanced course which introduces the Navier-Stokes equations as the basic model of fluid mechanics, and adaptive finite element methods to compute approximate solutions. The overall aim is the introduction of a new approach to computational turbulence modelling referred to as General Galerkin (G2) or Direct FEM Simulation (DFS) which enables cheap adaptive parameter-free prediction of aerodynamic forces at high Reynolds number using a residual based stabilisation as turbulence model [1]. Further, a new model for turbulent flow separation with a slip boundary condition together with detailed DFS computations enables the understanding of the fundamental mechanics of flight [2].

The theoretical parts of the course concern stability analysis of the numerical method, and goal oriented a posteriori error estimation. Practical parts of the course focus on computer implementation of finite element methods for the Navier-Stokes equations in the FEniCS automated framework for solution of partial differential equations [3], including adaptive mesh refinement, and applications of the methods on supercomputers.

The general aim is that the students should learn to analyse and use adaptive finite element technology to model fluid dynamics at high Reynolds numbers. After the course the students should be able to:

* account for the concepts of weak solution and weak uniqueness

* derive energy estimates for the underlying equations and DFS approximations

* derive a posteriori error estimates for output in DFS by means of duality

* analyse the global effect of skin friction boundary conditions in DFS computations

* use FEniCS software for adaptive flow computations with error control.

The main focus of the course is high Reynolds number incompressible flow and the following fundamental problems:

- turbulence

- flow separation

- generation of drag and lift in aerodynamics

with applications in a multitude of domains, such as vehicle, ship and aircraft aerodynamics, aerodynamics of ball sports, and flow in urban environments.

**Organizers and lecturers:**
Johan JANSSON (BCAM and KTH)

Johan HOFFMAN (KTH and BCAM)

**Website:**
http://www.bcamath.org/en/workshops/ntf
**References:**
[1] Johan Hoffman, Johan Jansson, Niclas Jansson, Rodrigo Vilela De Abreu, Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation, Computer Methods in Applied Mechanics and Engineering, 2015

[2] Johan Hoffman, Johan Jansson, Claes Johnson, New Theory of Flight, Journal of Mathematical Fluid Mechanics, 2015

[3] Johan Hoffman, Johan Jansson, Niclas Jansson, FEniCS-HPC: Automated predictive high-performance finite element computing with applications in aerodynamics, Proceedings of the 11th International Conference on Parallel Processing and Applied Mathematics, PPAM 2015. Lecture Notes in Computer Science, 2015

[4] Johan Hoffman, Johan Jansson, Niclas Jansson, Rodrigo Vilela de Abreu, and Claes Johnson, Computability and Adaptivity in CFD, Encyclopedia of Computational Mechanics. 2016

**Schedule for the BCAM Summer School on Advanced Computation in Fluid Mechanics - "New Theory of Flight":**
**Day 1:**
Start 10:00 at BCAM

Direct FEM Simulation (DFS) methodology

Adaptivity

Stabilization

Introduction to the FEniCS automated FEM software framework

Lab work in FEniCS: Python interface, DFS, adaptivity

**Day 2:**
Start 10:00 at BCAM

Flight simulation in DFS

New Theory of Flight

Optimal control (lecture by Roland Becker from Pau)

Lab work in FEniCS-HPC: turbulent flow with adaptive error control

**Day 3:**
Joint excursion in the Basque Country, e.g. Guggenheim/San Sebastian

Longer simulations can run during the day.

However, we kindly ask you make your

**INSCRIPTION**, (just below the info of this activity on the site of workshops on the web of BCAM), if you plan to participate.