4Numerical Simulation of Multi-Physics Systems
Summary
This chapter introduces the fundamental principles of numerical simulation of multi-physics systems – the next stage after modeling. Once built, the models must be transformed so that the computer can determine how the variables of interest evolve over time. Although these transformation and simulation stages are almost always automated, an understanding of how they operate will help the reader better grasp the simulation results. The bond graph formalism is introduced in view of the graphical presentation of the assignment of model causality. Furthermore, this chapter discusses the main sources of error in modeling and simulation.
Learning outcomes
On completing this chapter, the reader is expected to acquire knowledge on the following:
- – various types of equations and the classification of systems of equations;
- – advantages of time integration compared to differentiation;
- – model transformations required for simulation: causation and sequencing;
- – graphical approach of the previous point: bond graphs;
- – various time integration methods;
- – the main sources of error in numerical modeling and simulation.
4.1. From mathematical model to numerical model
Mathematical modeling of physical systems involves, almost inevitably, differential/integral relationships with respect to time, as soon as the modeler takes an interest in the non-static states of the studied system.
Typically, this is well illustrated by the equations ...
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