Stefan Heinz Libros

The book delves into the complexities of modeling turbulence in technological and environmental flows, highlighting the limitations of traditional deterministic equations, especially in reactive flow simulations. It advocates for stochastic models that capture the randomness of turbulence, offering a promising alternative to overcome closure issues found in deterministic methods. However, it emphasizes that implementing these stochastic approaches poses challenges, particularly in the numerical solutions required for industrial flow calculations, which often involve extensive grid cell considerations.

The book provides a comprehensive exploration of modeling techniques, starting with fundamental concepts rooted in analytical methods in Part I. It then transitions to Part II, which focuses on simulation methods designed to address various research challenges. This structured approach equips readers with essential tools and solutions for effective modeling in diverse contexts.

Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.