Spectral/hp Element Methods for Computational Fluid Dynamics (2nd edn)
Spectral/hp Element Methods for Computational Fluid Dynamics (2nd edn)
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Abstract
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. This book, an updated edition on the original text, presents the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text introduces 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.
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Front Matter
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1
INTRODUCTION
George Em Karniadakis andSpencer J. Sherwin
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2
FUNDAMENTAL CONCEPTS IN ONE DIMENSION
George Em Karniadakis andSpencer J. Sherwin
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3
MULTI-DIMENSIONAL EXPANSION BASES
George Em Karniadakis andSpencer J. Sherwin
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4
MULTI-DIMENSIONAL FORMULATION
George Em Karniadakis andSpencer J. Sherwin
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5
DIFFUSION EQUATION
George Em Karniadakis andSpencer J. Sherwin
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6
ADVECTION AND ADVECTION DIFFUSION
George Em Karniadakis andSpencer J. Sherwin
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7
NON-CONFORMING ELEMENTS
George Em Karniadakis andSpencer J. Sherwin
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8
ALGORITHMS FOR INCOMPRESSIBLE FLOWS
George Em Karniadakis andSpencer J. Sherwin
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9
INCOMPRESSIBLE FLOW SIMULATIONS: VERIFICATION AND VALIDATION
George Em Karniadakis andSpencer J. Sherwin
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10
HYPERBOLIC CONSERVATION LAWS
George Em Karniadakis andSpencer J. Sherwin
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End Matter
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