This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.

This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.

Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications - Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions

An invaluable instrument for gaining a wide-ranging perspective on the latest developments in mathematical aspects of scientific computing, discovering new applications and the most recent developments in long-standing applications. Provides an insight into the state of the art of Numerical Mathematics and, more generally, into the field of Advanced Applications.

Progress in Computational Physics is an e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories. In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume. Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems. The third volume - Novel Trends in Lattice Boltzmann Methods - Reactive Flow, Physicochemical Transport and Fluid-Structure Interaction - contains 10 chapters devoted to mathematical analysis of different issues related to the lattice Boltzmann methods, advanced numerical techniques for physico-chemical flows, fluid structure interaction and practical applications of these phenomena to real world problems.