Spectral/hp Element Methods for Computational Fluid Dynamics

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Spectral methods have been widely used in direct and large eddy simulation of turbulent flows, but their application in complex-geometry computational domains has been limited. Recently, the demand for accurate solutions to viscous flow equations around intricate configurations has spurred the development of high-order discretisation procedures on unstructured meshes, which are more efficient for time-dependent oscillatory solutions over extended periods. This updated and expanded edition presents significant advancements in multi-domain spectral methods, encompassing both fundamental and applied aspects. With over 50% new content, it includes topics such as discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and various stabilisation and filtering techniques. The text aims to introduce a broader audience to spectral/hp element methods, focusing on their application to unstructured meshes. It offers a thorough explanation of the key concepts behind these methods, along with practical examples of their derivation and application. The book is intended for students, academics, and practitioners in fields such as computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering, and climate/ocean modelling.