# Modelling & Simulation

Mathematical modelling and simulation provides an abstract environment with which to exhaustively explore the behaviour of real world systems and their potential responses to external stimuli, whilst minimising real world risk and cost of implementation. This module enables individuals to set up simple mathematical models and to interpret their results and those of others critically.

This module forms part of the Jaguar Land Rover MSc course in Automotive Engineering.

### Module Aims

The aims of this module are to:

• Develop a detailed theoretical and practical understanding of the derivation of ordinary differential equations to build models using both a block diagram approach and object oriented modelling.
• Develop the ability of course attendees to choose the most applicable numerical methods and techniques to obtain solutions that avoid simulation errors and algebraic loops.
• Develop a detailed theoretical and practical understanding of the principle of model causality and an ability to analyse and predict transient behaviour.
• Develop the ability of course attendees to determine the best choice of appropriate modelling and simulation tools and techniques for a given use-case, including the choice of solver that optimises simulation performance.

### Learning Outcomes

By the end of the module the student should be able to:

• Demonstrate a comprehensive practical application of the different approaches to advanced mathematical modelling.
• Evaluate and distinguish between a range of numerical methods and evaluate the correct usage for each.
• Demonstrate a sound understanding of stability analysis and numerical errors.
• Work independently in evaluating the practical effects of solver choice versus simulation performance through advanced approaches such as model reduction.
• Demonstrate a conceptual understanding of model causality and implement it on representative models.
• Develop integrated models to gain a practical understanding of current multi physics simulation techniques.

### Syllabus

• Introduction to Differential Equation Mathematical Modelling
• State Variable Block Diagram Modelling & Object Oriented Modelling
• Eigen values calcaluation, Numerical Integration Methods (Explicit/Implicit),
Solver selection (continuous/non-linear/stiff) and Simulation Stability
• Simulation Methods (Co-Simulation/Embedded/Real Time Application)
• 1D Multi Physics System Simulation
(Electrical/Mechanical/Hydraulic/Control System) and Correlation
Develop a detailed theoretical and practical understanding of the derivation of ordinary differential equations to build models using both a block diagram approach and object oriented modelling.

Develop the ability of course attendees to choose the most applicable numerical methods and techniques to obtain solutions that avoid simulation errors and algebraic loops.

Develop a detailed theoretical and practical understanding of the principle of model causality and an ability to analyse and predict transient behaviour.

Develop the ability of course attendees to determine the best choice of appropriate modelling and simulation tools and techniques for a given use-case, including the choice of solver that optimises simulation performance.