Principles of Computational Fluid Dynamics
An account is given of the present state of the art of computational fluid dynamics for graduate students, researchers, engineers and physicists. The underlying numerical principles are treated with a fair amount of detail, using elementary methods.
Format: Hardcover, English, 642 pages |
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Book Description
The book is aimed at graduate students, researchers, engineers and physicists involved in fluid computations. An up-to-date account is given of the present state-of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary methods. Attention is given to the difficulties arising from geometric complexity of the flow domain. Uniform accuracy for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Unified methods for compressible and incompressible flows are discussed. A treatment of the shallow-water equations is included. A basic introduction is given to efficient iterative solution methods. Many pointers are given to the current literature, facilitating further study.
Publisher Comments
The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state of the art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary methods.
Attention is given to the difficulties arising from geometric complexity of the flow domain. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. A treatment of the shallow-water equations is included. The theory of hyperbolic conservation laws is highlighted. Godunov's order barrier and how to overcome it by means of slope-limited schemes is discussed. A basic introduction is given to efficient iterative solution methods, using Krylov subspace and multigrid acceleration. Many pointers are given to the current literature, helping the reader to quickly reach the current research frontier. Matlab software is freely available at http://ta.twi.tudelft.nl/nw/users/wesseling
Reader Comments
mechanical eng.
principles of computational fluid dynamics
Table of Contents
Preface | V | |
1. | The basic equations if fluid dynamics | 1 |
1.1 | Introduction | 1 |
1.2 | Vector analysis | 5 |
1.3 | The total derivative and the transport theorem | 9 |
1.4 | Conservation of mass | 12 |
1.5 | Conservation of momentum | 13 |
1.6 | Conservation of energy | 19 |
1.7 | Thermodynamic aspects | 22 |
1.8 | Bernoulli's theorem | 26 |
1.9 | Kelvin's circulation theorem and potential flow | 28 |
1.10 | The Euler equations | 32 |
1.11 | The convection-diffusion equation | 33 |
1.12 | Conditions for incompressible flow | 34 |
1.13 | Turbulence | 37 |
1.14 | Stratified flow and free convection | 43 |
1.15 | Moving frame of reference | 47 |
1.16 | The shallow-water equations | 48 |
2. | Partial differential equations: analytic aspects | 53 |
2.1 | Introduction | 53 |
2.2 | Classification of partial differential equations | 54 |
2.3 | Boundary conditions | 61 |
2.4 | Maximum principles | 66 |
2.5 | Boundary layer theory | 70 |
3. | Finite volume and finite difference discretization on nonuniform grids | 81 |
3.1 | Introduction | 81 |
3.2 | An elliptic equation | 82 |
3.3 | A one-dimensional example | 84 |
3.4 | Vertex-centered discretization | 88 |
3.5 | Cell-centered discretization | 94 |
3.6 | Upwind discretization | 96 |
3.7 | Nonuniform grids in one dimension | 99 |
4. | The stationary convection-diffusion equation | 111 |
4.1 | Introduction | 111 |
4.2 | Finite volume discretization of the stationary convection-diffusion equation in one dimension | 113 |
4.3 | Numerical experiments on locally refined one-dimensional grid | 120 |
4.4 | Schemes of positive type | 122 |
4.5 | Upwind discretization | 126 |
4.6 | Defect correction | 129 |
4.7 | Peclet-independent accuracy in two dimensions | 133 |
4.8 | More accurate discretization of the convection term | 148 |
5. | The nonstationary convection-diffusion equation | 163 |
5.1 | Introduction | 163 |
5.2 | Example of instability | 164 |
5.3 | Stability definitions | 166 |
5.4 | The discrete maximim principle | 170 |
5.5 | Fourier stability analysis | 171 |
5.6 | Principles of von Neumann stability analysis | 174 |
5.7 | Useful properties of the symbol | 178 |
5.8 | Derivation of von Neumann stability conditions | 184 |
5.9 | Numerical experiments | 208 |
5.10 | Strong stability | 217 |
6. | The incompressible Navier-Stokes equations | 227 |
6.1 | Introduction | 227 |
6.2 | Equations of motion and boundary conditions | 227 |
6.3 | Spatial discretization on colocated grid | 232 |
6.4 | Spatial discretization on staggered grid | 240 |
6.5 | On the choice of boundary conditions | 244 |
6.6 | Temporal discretization on staggered grid | 249 |
6.7 | Temporal discretization on colocated grid | |
7. | Iterative methods | 263 |
7.1 | Introduction | 263 |
7.2 | Stationary iterative methods | 264 |
7.3 | Krylov subspace methods | 270 |
7.4 | Multigrid methods | 285 |
7.5 | Fast Poisson solvers | 292 |
7.6 | Iterative methods for the incompressible Navier-Stokes equations | 293 |
8. | The shallow water equations | 305 |
8.1 | Introduction | 305 |
8.2 | The one-dimensional case | 305 |
8.3 | The two-dimensional case | 323 |
9. | Scalar conservation laws | 339 |
9.1 | Introduction | 339 |
9.2 | Godunov's order barrier theorem | 339 |
9.3 | Linear schemes | 346 |
9.4 | Scalar conservation laws | 361 |
10. | The Euler equations in one space dimension | 397 |
10.1 | Introduction | 397 |
10.2 | Analytic aspects | 397 |
10.3 | The approximate Riemann solver of Roe | 414 |
10.4 | The Osher scheme | 425 |
10.5 | Flux splitting schemes | 436 |
10.6 | Numerical stability | 442 |
10.7 | The Jameson-Schmidt-Turkel scheme | 447 |
10.8 | Higher order schemes | 456 |
11. | Discretization in general domains | 467 |
11.1 | Introduction | 467 |
11.2 | Three types of grid | 467 |
11.3 | Boundary-fitted grids | 470 |
11.4 | Basic properties of grid cells | 474 |
11.5 | Introduction to tensor analysis | 484 |
11.5.1 | Invariance | 485 |
11.5.2 | The geometric quantities | 490 |
11.5.3 | Tensor calculus | 498 |
11.5.4 | The equations of motion in general coordinates | 501 |
12. | Numerical solution of the Euler equations in general coordinates | 503 |
12.1 | Introduction | 503 |
12.2 | Analytic aspects | 503 |
12.3 | Cell-centered finite volume discretization on boundary-fitted grids | 511 |
12.4 | Numerical boundary conditions | 518 |
12.5 | Temporal discretization | 525 |
13. | Numerical solution of the Navier-Stokes equations in general domains | 531 |
13.1 | Introduction | 531 |
13.2 | Analytic aspects | 531 |
13.3 | Colocated scheme for the compressible Navier-Stokes equations | 533 |
13.4 | Colocated scheme for the incompressible Navier-Stokes equations | 535 |
13.5 | Staggered scheme for the incompressible Navier-Stokes equations | 538 |
13.6 | An application | 557 |
13.7 | Verification and validation | 559 |
14. | Unified methods for computing incompressible and compressible flow | 567 |
14.1 | The need for unified methods | 567 |
14.2 | Difficulties with the zero Mach number limit | 568 |
14.3 | Preconditioning | 571 |
14.4 | Mach-uniform dimensionless Euler equations | 578 |
14.5 | A staggered scheme for fully compressible flow | 583 |
14.6 | Unified schemes for incompressible and compressible flow | 589 |
References | 603 | |
Index | 633 |
Related Book Categories
General Computational Fluid Dynamics