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 Institute 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






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.






 Please send an email to 



ECTS for Phd Students





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



logo cscs