Principles of Computational Fluid Dynamics -- CFD Books Guide

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
ISBN: 3540678530
Publisher: Springer-Verlag Berlin Heidelberg New York
Pub. Date: 2000
Edition: 1
Book Homepage: http://dutita0.twi.tudelft.nl/nw/users/wesseling/cfdbook.html

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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

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principles of computational fluid dynamics

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	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

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