Multiphysics modeling and computation of coupled and nonlinear problems, 5 credits

Prerequisites

Differential calculus, linear algebra, basic programming

Assessment

Assignment (project work in small groups)

Instruction

Lectures, lessons (programming)

Goals

This course presents nonlinear and coupled problems in continuum mechanics for solid bodies and fluids. By starting with the balance equations the so-called weak form is generated for various problems from mechanics, thermodynamics, and electromagnetism. Solutions for engineering problems are computed by using finite element method in space and finite difference method in time. All constitutive equations are going to be derived by using thermodynamical principles. The emphasis of this course is on a theoretical understanding of problems in continuum mechanics and their computations by applied mathematics. The best learning occurs by doing, hence, all problems are going to be computed by using open-source packages from FEniCS. After the course the student should be able to:

• Motivate and derive governing equations in engineering problems
• Develop a computational code for multiphysics simulations
• Numerically solve a system of coupled and nonlinear equations

Time

The course is planned for period 4, Spring 2024.

Contact

In case you have questions about the course, please contact B. Emek Abali:
b.emek.abali@angstrom.uu.se

Contents

12 lectures per 90 min + 2 world cafes (group assignment to show their results)

• Introduction to Python and FEniCS (editor, docker, Paraview)
• Linear and nonlinear elasticity, rheology in solids
• Flow of linear and nonlinear fluids
• Thermodynamics in viscous fluid and viscoelastic solid
• Electric conduction and polarized rigid body
• Balance equations with electromagnetic interaction
• Piezoelectric transducer

Literature

B. E. Abali. Computational Reality. Solving Nonlinear and Coupled Problems in Continuum Mechanics. Springer Nature, Singapore, 2017.