Spectral/hp Element Methods for CFD

Spectral/hp Element Methods for CFD

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Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.show more

Product details

  • Hardback | 402 pages
  • 162.6 x 236.2 x 35.6mm | 703.08g
  • Oxford University Press Inc
  • New York, United States
  • 140 line drawings, bibliography
  • 0195102266
  • 9780195102260

Table of contents

1. Introduction; 1.1 The Basic Equations of Fluid Dynamics; 1.2 Numerical Discretisation; 2. Fundamental Concepts and One-Dimensional Formulation; 2.1 Method of Weighted Residuals; 2.2 Galerkin Formulation; 2.3 One-Dimensional Expansion Bases; 2.4 Numerical Integration; 2.5 Differentiation; 2.6 Convergence Examples; 3. Multi-Dimensional Expansion Bases; 3.2 Expansions in Unstructured Domains; 3.3 Expansions in Homogenous Domains; 4. Multi-Dimensional Formulation; 4.1 Local Elemental Operations; 4.2 Global Operations; 4.3 Boundary Representation; 5. Geometrically Non-Conforming Elements; 5.1 The Need for Local Refinement; 5.2 Interface Conditions and Implementation; 5.3 Iterative Patching; 5.4 Constrained Approximation; 5.5 Mortar Patching; 6. Advection Equation; 6.1 Galerkin Discretisation; 6.2 Temporal Discretisation; 6.3 Eigen-Spectrum of the Galerkin Advection Operator; 6.4 Discontinuous Galerkin Discretisation; 6.5 Convergence; 7. Helmholtz Equation; 7.1 Galerkin Discretisation; 7.2 Eigen-Spectrum of Laplacian Operator; 7.3 Convergence; 7.4 Non-Smooth Domains; 7.5 Mixed and Discontinuous Galerkin Discretisation; 8. Incompressible Flows; 8.1 Variational Formulation; 8.2 Coupled Methods for Primitive Variables; 8.3 Splitting Methods for Primitive Variables; 8.4 Velocity-Vorticity Formulation; 8.5 The Gauge Method; 9. Flow Simulations; 9.1 Exact Navier-Stokes Solutions; 9.2 Direct Numerical Simulations - DNS; 9.3 Largy Eddy Simulations - LES; 9.4 Dynamic (dDNS) Versus Static DNS; 10. Compressible Flows; 10.1 Discontinuous Solutions and High-Order; 10.2 Conservative Formulation; 10.3 Monotonicity; 10.4 Euler Equations; 10.5 Navier-Stokes Equations; 10.6 Shock Fitting Techniques; A Jacobi Polynomials; B Gauss-Type Integration; C Collocation Differentiation; D Continuous Expansion Basis; E Characteristic Flux Decomposition for the Euler Equationshow more

Review quote

Karniadakis & Sherwin's book admirably meets its aim to "introduce a wider audience to spectral/hp element methods" Journal of Fluid Mechanicsshow more

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