Aim

The course introduces to the numerical techniques currently adopted for the design and evaluation of biomedical devices and to the assessment of physio-pathologic states and surgical procedures. Within the course, the student will practice with two standard commercial codes aimed at structural and fluid-dynamics analysis, respectively. In the last part of the course, students will work in small groups and apply the acquired knowledge and competences by develping new projects.

Expected learning results

Knowledge: students are expected to acquire notions on continuum mechanics, on numerical techniques to solve partial differential equations, on the use of two software packages that well represent the standard commercial solvers in the field of structural mechanics and fluid dynamics, respectively.

Competences: students arte expected to learn how to use the acquire knowledge, including how to properly discretize a geometrical model based on the analysis to be perfoermed and how to make reasonable assumptions on the modelled system. They are also expected to become able to autonomously use finite element and finite volume solvers on real problems.

Course contents

The course is organized in two parts. In the first part, students will be introduced to the computational methods implemented in the two commercial codes with a mix of lectures and tutorials. The second part will be dedicated to the analysis of specific problems for fluid-dynamics and solid mechanics in the lecture room equipped with computational facilities.
The introductory part includes the following topics:
Introduction to computational mechanics: the different steps needed to perform a numerical simulation will be presented starting from the standard continuum equations to their discretization and solution; in this framework, the main features of the numerical methods used for the solution of partial derivative equations will be described and compared. In particular the solution schemes of the finite element and finite volume methods will be analyzed.
Principles of fluid mechanics simulation: the commercial package Ansys-Fluent will be introduced together with its capability to handle laminar and turbulent, steady and transient flows. In detail lectures will describe the way the linear algebraic form of the field equations can be achieved, the iterative methods for algebraic system solution, the upwinding schemes, the pressure-velocity coupling algorithms and how to check convergence and result accuracy.
Principles of solid mechanics simulations: the commercial package Abaqus will be introduced, the main steps for the problem solution including the boundary conditions, meshing algorithms and solution strategies will be reviewed for linear and non linear simulations. In detail, standard displacement-based approach will be introduced together with discretization strategies of governing equations, numerical integration issues and algorithms for solution of linear and non linear problems.
Access to the course

It should be noted that this is a limited number access course. The mandatory procedure for access request is described here: http://www.ccsbio.polimi.it/?page_id=27

Students will be evaluated at the end of the course on the basis of a written examination on the theoretical parts of the course and of a presentation (written and oral) of the discussion of the results related to the problem investigated in the Lab hours.