Clean Numerical Simulation

By: Shijun Liao

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Hardcover | 5 September 2023 | Edition Number 1

At a Glance

Hardcover
162 Pages

Dimensions(cm)
23.4 x 15.6 x 1.12

Hardcover

$305.75

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This book proposes a new strategy to gain "clean" reliable numerical simulations of chaos and turbulence, namely the Clean Numerical Simulation (CNS), which can greatly reduce numerical noises to a tiny level much smaller than that of true solutions so that numerical noises are negligible, and the corresponding numerical simulation is "clean" and thus reliable.

By means of the CNS, one can gain "clean" reliable numerical simulations of chaotic systems in a long enough interval of time. The CNS provides a much more reliable tool than ever to study chaotic and turbulent systems in various fields of science and engineering.

In this book, the author will describe the basic ideas of the CNS and illustrate the CNS as a new powerful tool for chaos and turbulence. Unlike traditional algorithms in single/double precision, the CNS can provide us the "clean" results of chaos and turbulence. Using these "clean" results as benchmark solutions, we can investigate many important scientific problems, such as the origin of macroscopic randomness, the influence of micro-level uncertainty and tiny external noises to chaos and turbulence, and so on.

Comparing the "clean" CNS results with those badly "polluted" by numerical noises, one can investigate the influence of database noises on machine learning. Through this application and more, the author illustrates the validity and potential of the CNS.

The CNS is as a new, powerful tool for chaos and turbulence. It opens a new door for us to enter a "clean" numerical world.

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