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Mathematical Modeling of Physical Systems
Last Updated: 2026-02-05 15:07:04
Abstract
The class offers a systematic approach to the creation of differential equation models of physical processes. Object-oriented modeling. Symbolic conversion of DAE models to ODE form. Bond graphs. Applications in: electrical circuits, mechanical systems, thermodynamics, chemical reactions.
Content
The class offers a systematic approach to the creation of differential equation models of physical processes. In a first phase, the modeling of electrical circuits as well as mechanical one-dimensional systems is being discussed. The presentation illuminates the commonalities at the base of such modeling tasks. It is being shown that such modeling tasks lead invariably to sets ofÊ coupled differential and algebraic equations. The symbolic algorithms by Pantelides (index reduktion) and Tarjan (BLT partitioning of sets of algebraically coupled equations) are subsequently explained. The symbolic algorithms by Kron (tearing of tighly coupled algebraic models) as well as the symbolic relaxation algorithm are being discussed. In the subsequent phase, bond graphs are being introduced as a tool for the systematic modeling of physical processes by means of energy flows. The modeling of electrical circuits as well as mechanical one-dimensional systems is then repeated using the new approach to modeling. This serves to show that bond graphs indeed simplify the modeling task and support the modeler in recognizing modeling errors in an early stage. Subsequently, the lecture deals with modeling multi-dimensional mechanical systems. Subsequently, the discussion focuses intensively on thermodynamics. Thereby, the modeling task is being enhanced to systems, in which multiple forms of energy occur simultaneously. In the sequel, the class discusses how convective flows can be modeled. This leads to a general systematic modeling methodology for physical systems with distributed parameters. Finally, the modeling of discontinuous processes shall be dealt with, such as electrical switching phenomena and mechanical impulses. It is being shown that the symbolic algorithms must be generalized in this case. Inline integration is offered as a tool that can support the symbolic transformation of such system models to simulation models that can be simulated in a computationally efficient manner.
General Information
- Language
- English
- Levels
- BSC , DS , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 15 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Mathematical Modeling of Physical Systems |
|
2 h weekly |
| exercise | Mathematical Modeling of Physical Systems |
|
1 h weekly |