**The Swiss Graduate Program**

**FoMICS "Foundations in Mathematics and Informatics for Computer**

**Simulations in Science and Engineering"**

**is pleased to announce a summer school**

**for graduate/PhD**

**students in the fields of data science and high performance computing:**

**FoMICS Block Course on Navier-Stokes equations and Fluid-Structure Interaction Analysis**

**11th March - 4th June, 2020**

The block course is supported and organized by** Swiss Graduate School FOMICS - "Foundations in Mathematics and Informatics for Computer Simulations in Science and Engineering”**, which is located at ICS.

The **I****nstitute of Computational Science (ICS) at the Università della Svizzera italiana **announces a course designed for **PhD and Master's students with knowledge of Functional Analysis** on fluid dynamics and fluid-structure interaction analysis.

The course, starting on** March 11th, 2020 ** is taught by Dr. Maria Giuseppina Chiara Nestola (ICS, ETH Zurich, CCMC) and will cover advanced** mathematical **and** numerical aspects** of **Navier-Stokes equations** and its **coupling with solid-dynamics equations**.

Please note that the course will continue after 20th April due to the suspension of in classroom teaching activities

__Important dates__

March 11 2020

April 29 2020

May 6-7, 13-14, 20, 27-28 2020

June 4 2020

The course is distributed on 10 lectures of 2:00h each

and will be held each Wednesday from 15:30 to 17:15 online on Microsoft Team

__Rationale__

Fluid-structure Interaction is a complex phenomenon occurring in several fields including cardiovascular engineering,

geophysics, and turbomachinery.

This course aims to review three important ingredients of the fluid structure-interaction problem which are **Navier-Stokes equations**, **Elastodynamics equations** and **their coupling**.

The course will be split into two parts: the first one will focus on the **theory** and the** numerical methods **for** Navier-Stokes equations**, whereas the second part will focus on the **theory** and the **numerical methods **for the** fluid-structure Interaction problem**.

__Detailed Program__

**Block on Navier-Stokes equations for incompressible fluids **

Lesson 1 |
Navier-Stokes Equations: linear momentum equations (conservative and nonconservative forms), mass conservation equation, energy equations, Newtonian fluids, Nondimensionalization of the equations (Prandtl and Reynolds number) |

Lesson 2 |
Stationary Stokes problem: weak formulation, inf-sup condition, some considerations on boundary conditions, finite element approximation |

Lesson 3 |
Stationary Stokes problem: finite element approximation, algebraic representation of the problem and of the inf-sup condition. |

Lesson 4 |
Stationary Stokes problem: Convergence analysis, Stability analysis, Solver strategies (Uzawa algorithm, Krylov method and GMRES) |

Lesson 5 |
Stationary Navier-Stokes Problem: Weak Formulation, Finite element approximation, convergence analysis and algebraic representation |

**Block on Fluid Structure Interaction Problems**

Lesson 1 |
Non stationary Navier-Stokes equations: weak formulation, finite element approximation, time discretization |

Lesson 2 |
Elastodynamic equations: weak formulation, finite element approximation, time discretization (Newmark method, middle point) |

Lesson 3 |
Fluid-Structure Interaction Problem: Variational Formulations, energy estimates, added mass effect |

Lesson 4 |
Solutions Strategies: Arbitrary Lagrange-Eulerian Methods, Immersed Boundary Method, Fictitious Domain Methods. |

Lesson 5 |
Applications: a brief introduction to cardiovascular applications. |

__Registration__

__ECTS for Phd Students__

2

**Organizers**

Maria Giuseppina Chiara Nestola (USI-ICS/ETHZ/CCMC) Rolf Krause(USI-ICS)