Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. Here Karniadakis and Sherwin present a much-updated and expanded version of their successful first edition covering the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing over 50% new material, including discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text aims to introduce a wider audience to the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application, and is aimed at students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.

Fluid flow through small channels has become a popular research topic due to the emergence of biochemical lab-on-the-chip systems and microelectromechanical system fabrication technologies, which began in the late 1980's. There has been significant progress in the development of microfluidics and nanofluidics both at the application as well as at the fundamental and simulation levels in the last few years. This book provides a comprehensive summary of using computational tools to describe fluid flow in micro and nano configuration. This new version of the original book now covers length scales from Anstroms to microns (and beyond). The authors have maintained the emphasis on fundamental concepts with a mix of semianalytical, experimental and numerical results, and have outlined their relevance to modelling and analyzing functional devices. The material is devided into the three main categories of gas flows, liquid flows, and simulation techniques. The book contains many new developments and information has been updated and modified throughout. flow field as well as for electrical or mechanical engineers or physicists who need to incorporate flow modeling into their work. Review of earlier book by Karniadakis/Beskok on Microflows: For those who want to compute flows at the micro scale, this monograph is a must. It describes the state of the art and helps by providing coefficients, such as are] needed in situations of slip. Those who wonder what new fluid dynamics there is in the microworld are served by the overview of theory and treasures of numerical methods.EUROPEAN JOURNAL OF MECHANICS B / FLUID

This monograph focusing on gas flows addresses mostly theoretical issues and develops semi-analytical models as well as numerical methods for stimulating micro flows. It is appropriate for researchers in fluid mechanics interested in this new flow field as well as for electrical or mechanical engineers or physicists who need to incorporate flow modeling into their work. From the reviews: "For those who want to compute flows at the micro scale, this monograph is a must. It describes the state of the art and helps by providing coefficients, such as [are] needed in situations of slip. Those who wonder what new fluid dynamics there is in the microworld are served by the overview of theory and treasures of numerical methods." ?EUROPEAN JOURNAL OF MECHANICS B / FLUIDS