Abstract
Numerical simulations are used for the approximate prediction of situations under strictly defined conditions. They are based on mathematical models and represent interdependencies in the form of algorithms and computer programs. In everyday life, they are now ubiquitous for everyone, for example in weather forecasts or economic growth forecasts. In politics, they serve as an important tool for decision-making. In the scientific context, however, simulations are much more than a prediction tool. Similar to experiments, they also serve to build models themselves and thus enable the elucidation of causal relationships. Due to increasingly powerful computers, the importance of numerical simulation in science has grown steadily and rapidly over the last 50 years. In the meantime, it is considered an indispensable tool for gaining knowledge in many scientific disciplines. It is to be expected that numerical simulation will continue to grow rapidly in importance in the future and produce further surprising findings and technolo gies.
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Notes
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Identifying here is to be understood as assigning and recognizing and at most as a weakened equating.
- 6.
Underlying the averaging procedure is the law of large numbers, which states that the relative frequency of an event approaches the theoretical probability, on the premise of repetition under the same conditions.
- 7.
An example of a stochastic model is a micromodel for describing the movement of pedestrians. This can be used, for example, to predict evacuations at mass events. Here, for example, the change in direction of each individual pedestrian is described by a random variable. The flow models on which weather forecasts are based are usually deterministic in nature.
- 8.
Ortlieb, CP. (2000). Exakte Naturwissenschaft und Modellbegriff. Hamburger Beiträge zur Modellierung und Simulation. Retrieved from http://www.math.unihamburg.de/home/ortlieb/hb15exaktnatmod.pdf (July 15, 2000).
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Ortlieb, CP. (2001). Mathematische Modelle und Naturerkenntnis. Retrieved from http://www.math.uni-hamburg.de/home/ortlieb/hb16Istron.PDF (May 2001).
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Krause, M.J. (2010). Fluid Flow Simulation and Optimisation with Lattice Boltzmann Methods on High Performance Computers: Application to the Human Respiratory System. PhD thesis, Karlsruhe Institute of Technology (KIT), Universität Karlsruhe (TH), Kaiserstraße 12, 76131 Karlsruhe, Germany, July 2010. Retrieved from http://digbib.ubka.uni-karlsruhe.de/volltexte/1000019768, Section 3.
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Ibid., section 4.
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Krause, M.J. (2023). Through Numerical Simulation to Scientific Knowledge. In: Schweiker, M., Hass, J., Novokhatko, A., Halbleib, R. (eds) Measurement and Understanding in Science and Humanities. Palgrave Macmillan, Wiesbaden. https://doi.org/10.1007/978-3-658-36974-3_16
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