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Course Topics
List of topics covered Modeling and simulating: Calculation vs. simulation. Model accuracy. Model validation. Model definition: Definition of model for physical systems. Analytical vs numerical solutions. Model refinement and extension. Finite difference approaches: Solution of partial derivatives differential equations with finite difference approaches. Consistency, stability and convergence. First order schemes (forward, backward). Second order schemes (central, Crank-Nicolson) Applications: Development of case studies. Examples from thermal and thermodynamic systems. Modelling of systems and solutions of control problems.

Teaching format
Lectures (blackboard and/or slides) and spreadsheet implementation.

Educational objectives
(1) Knowledge and understanding: - Modelling and simulation vs calculations - Derivation of models for physical systems - Numerical solutions of differential equations (2) Applying Knowledge and understanding: - Defining models for case studies - Applying simulations to understand system behavior - Calculating multiple performance aspects (3) Making judgments: - Comparing different modelling approaches - Deciding the degree of accuracy required for the specific application - Optimizing the design or behavior of a system using modelling approaches (4) Communication skills: - Using the appropriate technical vocabulary related to the topic - Preparing a report representing and summarizing complex results and providing appropriate interpretation (5) Learning skills: - Decomposing a complex problem into sub- problems - Finding the analytical expression and the numerical solution - Comparing different methods and sources

Evaluation criteria
Marks are attributed according to the following assessment aspects: - Synthesis ability to explain the fundamental aspects of the problem (0=nothing, 1=insufficient; 2=sufficient; 3=full) - Analysis ability to describe details and specific formulas/models (0=nothing, 1=insufficient; 2=sufficient; 3=full) - Application ability to implement the principles and formulas and to solve practical cases (0=nothing, 1=insufficient; 2=sufficient; 3=full) - Reporting ability to represent and summarize the main results and to provide an appropriate interpretation