1 Organization

Goal of the lecture

This lecture provides an introduction to

continuum mechanical modeling from the perspective of simulation science and computational engineering.

Starting from fundamentals and balance laws, we consider

important classes of mathematical models

for transport, flow and multiphysics processes. We also discuss

complexity reduction strategies

such as homogenization and depth-averaging to enable the simulation of porous media flow, free-surface flow and solid-liquid phase change processes.

Complementary theoretical and programming exercises

help to consolidate the content of this lecture and provide theoretical and application-oriented examples.

Lecture

Target audience:

  • Simulation Sciences
  • Computational Engineering Sciences
  • Computer Science

Required preliminary knowledge:

  • Calculus and linear algebra
  • Basic knowledge of numerical methods for partial differential equations, e.g. acquired through NumPDE
  • Basic knowledge in fluidmechanics and thermodynamics is an advantage, but no must.

Lecture

Time slots:

  • 🕣 Monday, 8:30 - 10:00, 📍 Eilfschornsteinstr. 18, Room 009
  • 🕣 Friday, 8:30 - 10:00, 📍 Eilfschornsteinstr. 18, Room 009

Schedule is displayed on https://mbd.pages.rwth-aachen.de/courses/cmm/


Note

Any short notice changes will be communicated via moodle!

Exercises

Time slots:

  • 🕣 Friday, 14:30 - 16:00, 📍 Eilfschornsteinstr. 18, Room 009


Figure 1: Ingo Steldermann (steldermann@…)
Figure 2: Benjamin Terschanski (terschanski@…)
Figure 3: Alan Correa (correa@…)
  • Weekly exercises will start this week
  • Structure and assignment-based bonus point system will be introduced in the first exercise

Further organization

Exams

  • 🕣 05.08.2025, 09:00 – 11:00, 📍 (FT (2090|120) Melatener Str. 23-25, 1.Obergeschoß)
  • Bonus points via homeworks -> details will be provided during exercises
  • Old exams can be found on our webpage -> note evolution of exam structure


Material and resources:

  • Announcements are sent out and archived via moodle!
  • Script, slides and exercises will be made available via our lecture webpage:

https://mbd.pages.rwth-aachen.de/courses/cmm/

2 Motivation

Simulation sciences are a key enabling technology

Objectives inherent to many societal challenges require fundamental understanding of the underlying physical processes, systems thinking, and advanced compute methods!


Figure 4: Addressing societal challenges requires proficiency in simulation science and computational science and engineering

Simulation sciences are a key enabling technology

Objectives inherent to many societal challenges require fundamental understanding of the underlying physical processes, systems thinking, and advanced compute methods!


Figure 5: Addressing societal challenges requires proficiency in simulation science and computational science and engineering

3 Modeling example

Modeling solid-liquid phase-change: The Stefan problem

Figure 6: Milestone contribution to the modeling of phase-change processes due to Stefan, 1891

Stefan’s solution cannot capture all processes


Figure 7: Measuring phase-change processes

Stefan’s solution cannot capture all processes

Figure 8: Measuring phase-change processes

Stefan’s solution cannot capture all processes

We need to develop physics-based continuum mechanical computational models at a problem specific fidelity.

Figure 9: Measuring phase-change processes

4 Computational modeling

What is a model?

A model is a purposeful idealization and abstraction of our perception of reality.


Figure 10: Idealization reduces complexity and facilitates feasibility.
Figure 11: Abstraction reduces a complex system to its essential parts and facilitates transfer.

What is a model?

In simulation science and computational engineering, the purpose often implies an I/O character.


Figure 12: Relevant models often have an I/O character

Computational model development cycle

Figure 13: Verification and Validation in CE

5 Structure of the lecture

Content overview

Overview of the lecture

References

Gonzalez, Oscar, and Andrew M. Stuart. 2001. A First Course in Continuum Mechanics. 1st ed. Cambridge University Press. https://www.cambridge.org/core/product/identifier/9780511619571/type/book.