Computational fluid dynamics: principles and applications

Front Cover; Computational Fluid Dynamics: Principles and Applications; Copyright; Contents; Acknowledgments; List of Symbols; Abbreviations; Chapter 1: Introduction; Chapter 2: Governing Equations; 2.1 The Flow and Its Mathematical Description; 2.1.1 Finite control volume; 2.2 Conservation Laws; 2.2.1 The continuity equation; 2.2.2 The momentum equation; 2.2.3 The energy equation; 2.3 Viscous Stresses; 2.4 Complete System of the Navier-Stokes Equations; 2.4.1 Formulation for a perfect gas; 2.4.2 Formulation for a real gas; 2.4.3 Simplifications to the Navier-Stokes equations.

Thin shear layer approximationParabolized Navier-Stokes equations; Euler equations; References; Chapter 3: Principles of Solution of the Governing Equations; 3.1 Spatial Discretization; 3.1.1 Finite-difference method; 3.1.2 Finite-volume method; 3.1.3 Finite-element method; 3.1.4 Other discretization methods; Spectral-element method; Lattice Boltzmann method; Gridless method; 3.1.5 Central and upwind schemes; Central schemes; Upwind schemes; Flux-vector splitting schemes; Flux-difference splitting schemes; TVD Schemes; Fluctuation-splitting schemes; Solution reconstruction.

First- and second-order schemesENO/WENO Schemes; Central versus upwind schemes; Upwind schemes for real gas flows; 3.2 Temporal Discretization; 3.2.1 Explicit schemes; 3.2.2 Implicit schemes; 3.3 Turbulence Modeling; 3.4 Initial and Boundary Conditions; References; Chapter 4: Structured Finite-Volume Schemes; 4.1 Geometrical Quantities of a Control Volume; 4.1.1 Two-dimensional case; 4.1.2 Three-dimensional case; 4.2 General Discretization Methodologies; 4.2.1 Cell-centered scheme; 4.2.2 Cell-vertex scheme: overlapping control volumes; 4.2.3 Cell-vertex scheme: dual control volumes.

4.2.4 Cell-centered versus cell-vertex schemes4.3 Discretization of the Convective Fluxes; 4.3.1 Central scheme with artificial dissipation; Scalar dissipation scheme; Matrix dissipation scheme; 4.3.2 Flux-vector splitting schemes; Van Leer's scheme; AUSM; CUSP scheme; 4.3.3 Flux-difference splitting schemes; Roe upwind scheme; 4.3.4 Total variation diminishing schemes; Upwind TVD scheme; 4.3.5 Limiter functions; Limiter functions for MUSCL interpolation; MUSCL scheme with =0; MUSCL scheme with =1/3; Limiter for CUSP scheme; Limiter for TVD scheme; 4.4 Discretization of the Viscous Fluxes.

4.4.1 Cell-centered scheme4.4.2 Cell-vertex scheme; References; Chapter 5: Unstructured Finite-Volume Schemes; 5.1 Geometrical Quantities of a Control Volume; 5.1.1 Two-dimensional case; Triangular element; Quadrilateral element; Element center; 5.1.2 Three-dimensional case; Triangular face; Quadrilateral face; Volume; Cell centroid; 5.2 General Discretization Methodologies; 5.2.1 Cell-centered scheme; 5.2.2 Median-dual cell-vertex scheme; 5.2.3 Cell-centered versus median-dual scheme; Accuracy; Computational work; Memory requirements; Grid generation/adaptation.