Principles of computational fluid dynamics = 计算流体力学原理 /

preface .

1. the basic equations of 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
1.10 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: nalytic 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-diffuslon equation
5.1 introduction
5.2 example of instability
5.3 stability definitions
5.4 the discrete maximum 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
5.10 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 equa tions
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 geometric 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

domains
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 equa-

tions
13.4 colocated scheme for the incompressible navier-stokes equa-

tions
13.5 staggered scheme for the incompressible navier-stokes equa-

tions
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

references
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