High Accuracy Computing Methods
Fluid Flows and Wave Phenomena

This book presents topics in a single source format using unified spectral theory of computing.

Tapan Sengupta (Author)

9781107023635, Cambridge University Press

Hardback, published 16 May 2013

586 pages, 336 b/w illus. 9 tables
25 x 19 x 2.9 cm, 1.23 kg

This book presents topics in a single source format using unified spectral theory of computing. With developments of DNS and LES, practitioners are rediscovering waves as important in fluid flows, and capturing these numerically is central to high accuracy computing. Analysis of waves and its use in numerical methods in propagating energy at the right velocity (dispersion effects) and with right amplitude (dissipation) are essential. Most industrial codes using Reynolds-averaged Navier–Stokes equations with turbulence models cannot conceive of capturing waves. The new themes covered in this book are: • Correct error propagation analysis • Practical compact schemes and global analysis tool • Aliasing error and its alleviation • Spurious upstream propagating q-waves • Explanation of the Gibbs phenomenon • New 1D and 2D filters for LES/DNS without SGS modelling • Anisotropic skewed wave propagation • Development and analysis of dispersion relation preservation (DRP) schemes • Flow instabilities and wave propagation phenomena

Foreword
Preface
1. Introduction to scientific computing
2. Governing equations of fluid mechanics
3. Classification of quasi-linear partial differential equations
4. Waves and space-time dependence in computing
5. Spatial and temporal discretizations of partial differential equations
6. Solution methods for parabolic partial differential equations
7. Solution methods for elliptic partial differential equations
8. Solution of hyperbolic PDEs: signal and error propagation
9. Curvilinear coordinates and grid generation
10. Spectral analysis of numerical schemes and aliasing error
11. Higher accuracy and higher order methods
12. Introduction to finite volume and finite element methods
13. Solution of Navier–Stokes equations
14. Recent developments in discrete computing
Exercises
References.

Subject Areas: Mathematical theory of computation [UYA], Mechanics of fluids [TGMF], Fluid mechanics [PHDF], Applied mathematics [PBW]