Robust Computational Techniques for Boundary Layers

Paul Farrell, Alan Hegarty, John M. Miller, MD, FACR , Eugene O'Riordan

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English

Chapman & Hall/CRC
30 March 2000

Maths for scientists; Fluid mechanics; Wave mechanics (vibration & acoustics); Maths for computer scientists

Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They present a new numerical technique that provides precise results in the boundary layer regions for the problems discussed in the book. They show that this technique can be adapted in

a natural way to a real flow problem, and that it can be used to construct benchmark solutions for comparison with solutions found using other numerical techniques. Focusing on robustness, simplicity, and wide applicability rather than on optimality, Robust Computational Techniques for Boundary Layers provides readers with an understanding of the underlying

principles and the essential components needed for the construction of numerical methods for boundary layer problems. It explains the fundamental ideas through physical insight, model problems, and computational experiments and gives details of the linear solvers used in the computations so that readers can implement the methods and reproduce the numerical results.

By: Paul Farrell, Alan Hegarty, John M. Miller, MD, FACR, Eugene O'Riordan, Grigory I. Shishkin
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm, Spine: 18mm
Weight: 660g
ISBN: 9781584881926
ISBN 10: 1584881925
Pages: 256
Publication Date: 30 March 2000
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Introduction to Numerical Methods for Problems with Boundary Layers. Numerical Methods on Uniform Meshes. Layer Resolving Methods for Convection-Diffusion Problems in One Dimension. The Limitations of Non-Monotone Numerical Methods. Convection-Diffusion Problems in a Moving Medium. Convection-Diffusion Problems with Frictionless Walls. Convection-Diffusion Problems with No Slip Boundary Conditions. Experimental Estimation of Errors. Non-Monotone Methods in Two Dimensions. Linear and Nonlinear Reaction-Diffusion Problems. Prandtl Flow past a Flat Plate-Blasius' Method. Prandtl Flow past a Flat Plate-Direct Method. References. NTI/Sales Copy

Farrell, Paul; Hegarty, Alan; Miller, John M.; O'Riordan, Eugene; Shishkin, Grigory I.

Reviews for Robust Computational Techniques for Boundary Layers

"""In summary I think the early sections of the book give a very nice picture of the difficulties associated with singularly perturbed convection-diffusion problems. The insight gained from the structure of the uniform convergence proofs could be used to analyze different discretizations and mesh adaptations strategies. The extensive number of two-dimensional examples could also serve as a great source of benchmark solutions to test other approaches."" -SIAM Review vol. 43, no.3 (549-581)"