Spectral Methods

Following up the seminal Spectral Methods in Fluid Dynamics , this book surveys the essential algorithmic and theoretical aspects of spectral methods for complex geometries. This is a companion book to Spectral Methods: Fundamentals in Single Domains , which discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions.

Following up the seminal Spectral Methods in Fluid Dynamics, this book surveys the essential algorithmic and theoretical aspects of spectral methods for complex geometries. The chapter on spectral algorithms for incompressible flow is focused on those algorithms that have proven most useful in practice over the past two decades, has much greater coverage of algorithms for two or more non-periodic directions, and describes how to treat outflow boundaries. The material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting.

Most comprehensive and up-to-date theory and state-of-the-art algorithms of spectral methods for application in fluid dynamics and complex domains Authors pioneered Spectral Methods in Fluid Dynamics Calculations Monograph at forefront of research but addressing students as well Contains a Spectral Methods Primer. Can thus be read independently of the companion book "Spectral methods. Fundamentals in Single Domains Includes supplementary material: sn.pub/extras

Inhalt
Fundamentals of Fluid Dynamics.- Single-Domain Algorithms and Applications for Stability Analysis.- Single-Domain Algorithms and Applications for Incompressible Flows.- Single-Domain Algorithms and Applications for Compressible Flows.- Discretization Strategies for Spectral Methods in Complex Domains.- Solution Strategies for Spectral Methods in Complex Domains.- General Algorithms for Incompressible Navier-Stokes Equations.- Spectral Methods Primer.