01 December 2008

[yim261] Principles of Computational Fluid Dynamics-Wesseling

A text for graduate students, researchers, engineers and physicists working with flow computations. Gives an up-to-date account of the most current numerical methods employed in computational fluid dynamics. Gives special attention to stability analysis.

Table of Content :
1 The basic equations if fluid dynamics
1.1 Introduction
1.2 Vector analysis
1.3 The total derivative and the transport theorem
1.4 Conservation of mass
1.5 Conservation of momentum
1.6 Conservation of energy
1.7 Thermodynamic aspects
1.8 Bernoulli's theorem
1.9 Kelvin's circulation theorem and potential flow
1.1 The Euler equations
1.11 The convection-diffusion equation
1.12 Conditions for incompressible flow
1.13 Turbulence
1.14 Stratified flow and free convection
1.15 Moving frame of reference
1.16 The shallow-water equations

2 Partial differential equations: analytic aspects
2.1 Introduction
2.2 Classification of partial differential equations
2.3 Boundary conditions
2.4 Maximum principles
2.5 Boundary layer theory

3 Finite volume and finite difference discretization on nonuniform grids
3.1 Introduction
3.2 An elliptic equation
3.3 A one-dimensional example
3.4 Vertex-centered discretization
3.5 Cell-centered discretization
3.6 Upwind discretization
3.7 Nonuniform grids in one dimension

4 The stationary convection-diffusion equation
4.1 Introduction
4.2 Finite volume discretization of the stationary convection-diffusion equation in one dimension
4.3 Numerical experiments on locally refined one-dimensional grid
4.4 Schemes of positive type
4.5 Upwind discretization
4.6 Defect correction
4.7 Peclet-independent accuracy in two dimensions
4.8 More accurate discretization of the convection term

5 The nonstationary convection-diffusion equation
5.1 Introduction
5.2 Example of instability
5.3 Stability definitions
5.4 The discrete maximim principle
5.5 Fourier stability analysis
5.6 Principles of von Neumann stability analysis
5.7 Useful properties of the symbol
5.8 Derivation of von Neumann stability conditions
5.9 Numerical experiments
5.1 Strong stability

6 The incompressible Navier-Stokes equations
6.1 Introduction
6.2 Equations of motion and boundary conditions
6.3 Spatial discretization on colocated grid
6.4 Spatial discretization on staggered grid
6.5 On the choice of boundary conditions
6.6 Temporal discretization on staggered grid
6.7 Temporal discretization on colocated grid

7 Iterative methods
7.1 Introduction
7.2 Stationary iterative methods
7.3 Krylov subspace methods
7.4 Multigrid methods
7.5 Fast Poisson solvers
7.6 Iterative methods for the incompressible Navier-Stokes equations

8 The shallow water equations
8.1 Introduction
8.2 The one-dimensional case
8.3 The two-dimensional case

9 Scalar conservation laws
9.1 Introduction
9.2 Godunov's order barrier theorem
9.3 Linear schemes
9.4 Scalar conservation laws

10 The Euler equations in one space dimension
10.1 Introduction
10.2 Analytic aspects
10.3 The approximate Riemann solver of Roe
10.4 The Osher scheme
10.5 Flux splitting schemes
10.6 Numerical stability
10.7 The Jameson-Schmidt-Turkel scheme
10.8 Higher order schemes

11 Discretization in general domains
11.1 Introduction
11.2 Three types of grid
11.3 Boundary-fitted grids
11.4 Basic properties of grid cells
11.5 Introduction to tensor analysis
11.5.1 Invariance
11.5.2 The geometric quantities
11.5.3 Tensor calculus
11.5.4 The equations of motion in general coordinates

12 Numerical solution of the Euler equations in general coordinates
12.1 Introduction
12.2 Analytic aspects
12.3 Cell-centered finite volume discretization on boundary-fitted grids
12.4 Numerical boundary conditions
12.5 Temporal discretization

13 Numerical solution of the Navier-Stokes equations in general domains
13.1 Introduction
13.2 Analytic aspects
13.3 Colocated scheme for the compressible Navier-Stokes equations
13.4 Colocated scheme for the incompressible Navier-Stokes equations
13.5 Staggered scheme for the incompressible Navier-Stokes equations
13.6 An application
13.7 Verification and validation

14 Unified methods for computing incompressible and compressible flow
14.1 The need for unified methods
14.2 Difficulties with the zero Mach number limit
14.3 Preconditioning
14.4 Mach-uniform dimensionless Euler equations
14.5 A staggered scheme for fully compressible flow
14.6 Unified schemes for incompressible and compressible flow


  • Title : Principles of Computational Fluid Dynamics
  • Author : Pieter Wesseling
  • Publisher: Springer
  • Number Of Pages: 644
  • Publication Date: 2000-11-27
  • ISBN / ASIN: 3540678530
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