Robust computational techniques for boundary layers /
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| Imprint: | Boca Raton : Chapman & Hall/CRC, c2000. |
|---|---|
| Description: | xv, 254 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Applied mathematics ; 13 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4616427 |
Table of Contents:
- 1. Introduction to numerical methods for problems with boundary layers
- 1.1. The location and width of a boundary layer
- 1.2. Norms for boundary layer functions
- 1.3. Numerical methods
- 1.4. Robust layer-resolving methods
- 1.5. Some notation
- 2. Numerical methods on uniform meshes
- 2.1. Convection-diffusion problems in one dimension
- 2.2. Centred finite difference method
- 2.3. Monotone matrices and discrete comparison principles
- 2.4. Upwind finite difference methods
- 2.5. Fitted operator methods
- 2.6. Neumann boundary conditions
- 2.7. Error estimates in alternative norms
- 3. Layer resolving methods for convection diffusion problems in one dimension
- 3.1. Bakhvalov fitted meshes
- 3.2. Piecewise-uniform fitted meshes
- 3.3. Theoretical results
- 3.4. Global accuracy on piecewise-uniform meshes
- 3.5. Approximation of derivatives
- 3.6. Alternative transition parameters
- 4. The limitations of non-monotone numerical methods
- 4.1. Non-physical behaviour of numerical solutions
- 4.2. A non-monotone method
- 4.3. Accuracy and order of convergence
- 4.4. Tuning non-monotone methods
- 4.5. Neumann boundary conditions
- 4.6. Approximation of scaled derivatives
- 4.7. Further considerations
- 5. Convection-diffusion problems in a moving medium
- 5.1. Motivation
- 5.2. Convection-diffusion problems
- 5.3. Location of regular and corner boundary layers
- 5.4. Asymptotic nature of boundary layers
- 5.5. Monotone parameter-uniform methods
- 5.6. Computed errors and computed orders of convergence
- 5.7. Numerical results
- 5.8. Neumann boundary conditions
- 5.9. Corner boundary layers
- 5.10. Computational work
- 6. Convection-diffusion problems with frictionless walls
- 6.1. The origin of parabolic boundary layers
- 6.2. Asymptotic nature
- 6.3. Inadequacy of uniform meshes
- 6.4. Fitted meshes for parabolic boundary layers
- 6.5. Simple parameter-uniform analytic approximations
- 7. Convection-diffusion problems with no slip boundary conditions
- 7.1. No-slip boundary conditions
- 7.2. Width of degenerate parabolic boundary layers
- 7.3. Monotone fitted mesh method
- 7.4. Numerical results
- 7.5. Slip versus no-slip
- 8. Experimental estimation of errors
- 8.1. Theoretical error estimates
- 8.2. Quick algorithms
- 8.3. General algorithm
- 8.4. Validation
- 8.5. Practical uses of [epsilon]-uniform error parameters
- 8.6. Global error parameters
- 9. Non-monotone methods in two dimensions
- 9.1. Non-monotone methods
- 9.2. Tuned non-monotone method
- 9.3. Difficulties in tuning non-monotone methods
- 9.4. Weaknesses of non-monotone [epsilon]-uniform methods
- 10. Linear and nonlinear reaction-diffusion problems
- 10.1. Linear reaction diffusion problems
- 10.2. Semilinear reaction-diffusion problems
- 10.3. Nonlinear solvers
- 10.4. Numerical methods on uniform meshes
- 10.5. Numerical methods on piecewise-uniform meshes
- 10.6. An alternative stopping criterion
- 11. Prandtl flow past a flat plate - Blasius' method
- 11.1. Prandtl boundary layer equations
- 11.2. Blasius' solution
- 11.3. Singularly perturbed nature of Blasius' problem
- 11.4. Robust layer-resolving method for Blasius' problem
- 11.5. Numerical solution of Blasius' problem
- 11.6. Computed error estimates for Blasius' problem
- 11.7. Computed global error estimates for Blasius' solution
- 12. Prandtl flow past a flat plate - direct method
- 12.1. Prandtl problem in a finite domain
- 12.2. Nonlinear finite difference method
- 12.3. Solution of the nonlinear finite difference method
- 12.4. Error analysis based on the finest mesh solution
- 12.5. Error analysis based on the Blasius solution
- 12.6. A benchmark solution for laminar flow
- References
- Index
