Computational fluid dynamics.

*(English)*Zbl 1037.76001
Cambridge: Cambridge University Press (ISBN 0-521-59416-2/hbk; 978-0-511-60620-5/ebook). xxiii, 1012 p. (2002).

The author of this book, an important leader in the domain of computational fluid dynamics (CFD), was for some decades one of the most authoritative witnesses of the great progress in finite element methods (FEM), finite difference methods (FDM), finite volume methods (FVM) and other computational methods employed in the study of fluid flows. His enormous experience is shared both to beginners and to practitioners by the aid of this monography.

In Part One of the book the author presents the basic concepts of FDM, FEM and FVM. He also reviews the basic forms of partial differential equations and some of the governing equations in fluid dynamics, including nonconservative and conservative forms of Navier-Stokes equations.

Part Two presents the basic concepts of finite difference theory, various formulation strategies and applications to incompressible and compressible flows described by the potential, Euler or Navier-Stokes equations. The author presents various finite difference schemes for solutions of elliptic, parabolic, hyperbolic and Burgers’ equations. He also introduces FVM via FDM.

Part Three is devoted to FEM. After presenting the finite element formulations and finite element interpolation functions, one utilizes standard and generalized Galerkin methods for studying steady-state and transient linear problems. The nonlinear problems (convection-dominated flows) like Burgers’ equations and nonlinear wave equation are studied by means of Taylor-Galerkin, Petrov-Galerkin, least squares, and Newton-Raphson methods. The incompressible viscous flows are studied via FEM, using primitive variables and vortex methods. For studying the compressible flows the author utilizes generalized Galerkin, Taylor-Galerkin, generalized Petrov-Galerkin, characteristic Galerkin, discontinuous Galerkin, or combined FEM/FDM/FVM methods. Miscellanous weighted residual methods (spectral, least squares), and relationships between FDM, FEM and other methods are also discussed.

Part Four is devoted to automatic grid generation, adaptive methods and computing techniques. The author presents both the structured grid generation (algebraic methods, PDE mapping methods, surface grid generation) and the unstructured grid generation (Delaunay-Voronoi, advancing front, combined methods). Structured and unstructured adaptive methods are described together with the main computing techniques (domain decomposition methods, multigrid methods, parallel processing).

Part Five is devoted to applications. For study of turbulence the author presents the theoretical turbulence methods, large eddy simulation and direct numerical simulation. For studying chemically reactive flows and combustion, the author gives governing equations for reactive flows, for chemical equilibrium computations, discusses chemistry-turbulence interaction models, hypersonic reactive flows and gives some example problems. Then applications to acoustics are based on pressure, vorticity and entropy mode acoustics. The applications to combined mode radiative heat transfer are considered both in participating and nonparticipating media. For studying multiphase flows one presents the volume of fluid formulation with continuum surface force and fluid-particle mixture flows. The applications to electromagnetic flows are in the fields of magnetohydrodynamics, rarefied gas dynamics and semiconductor plasma processing. Finally, some applications to relativistic astrophysical flows are given.

The book ends with four appendices (three-dimensional flux Jacobians, Gaussian quadrature, two-phase flow source term, Jacobians for surface tension, relativistic astrophysical flow metrics, Christoffel symbols and FDV flux and source terms Jacobian). The book is recommended to people interested in computing methods, and especially to students and practitioners in mechanical, aerospace, chemical and civil engineering.

In Part One of the book the author presents the basic concepts of FDM, FEM and FVM. He also reviews the basic forms of partial differential equations and some of the governing equations in fluid dynamics, including nonconservative and conservative forms of Navier-Stokes equations.

Part Two presents the basic concepts of finite difference theory, various formulation strategies and applications to incompressible and compressible flows described by the potential, Euler or Navier-Stokes equations. The author presents various finite difference schemes for solutions of elliptic, parabolic, hyperbolic and Burgers’ equations. He also introduces FVM via FDM.

Part Three is devoted to FEM. After presenting the finite element formulations and finite element interpolation functions, one utilizes standard and generalized Galerkin methods for studying steady-state and transient linear problems. The nonlinear problems (convection-dominated flows) like Burgers’ equations and nonlinear wave equation are studied by means of Taylor-Galerkin, Petrov-Galerkin, least squares, and Newton-Raphson methods. The incompressible viscous flows are studied via FEM, using primitive variables and vortex methods. For studying the compressible flows the author utilizes generalized Galerkin, Taylor-Galerkin, generalized Petrov-Galerkin, characteristic Galerkin, discontinuous Galerkin, or combined FEM/FDM/FVM methods. Miscellanous weighted residual methods (spectral, least squares), and relationships between FDM, FEM and other methods are also discussed.

Part Four is devoted to automatic grid generation, adaptive methods and computing techniques. The author presents both the structured grid generation (algebraic methods, PDE mapping methods, surface grid generation) and the unstructured grid generation (Delaunay-Voronoi, advancing front, combined methods). Structured and unstructured adaptive methods are described together with the main computing techniques (domain decomposition methods, multigrid methods, parallel processing).

Part Five is devoted to applications. For study of turbulence the author presents the theoretical turbulence methods, large eddy simulation and direct numerical simulation. For studying chemically reactive flows and combustion, the author gives governing equations for reactive flows, for chemical equilibrium computations, discusses chemistry-turbulence interaction models, hypersonic reactive flows and gives some example problems. Then applications to acoustics are based on pressure, vorticity and entropy mode acoustics. The applications to combined mode radiative heat transfer are considered both in participating and nonparticipating media. For studying multiphase flows one presents the volume of fluid formulation with continuum surface force and fluid-particle mixture flows. The applications to electromagnetic flows are in the fields of magnetohydrodynamics, rarefied gas dynamics and semiconductor plasma processing. Finally, some applications to relativistic astrophysical flows are given.

The book ends with four appendices (three-dimensional flux Jacobians, Gaussian quadrature, two-phase flow source term, Jacobians for surface tension, relativistic astrophysical flow metrics, Christoffel symbols and FDV flux and source terms Jacobian). The book is recommended to people interested in computing methods, and especially to students and practitioners in mechanical, aerospace, chemical and civil engineering.

Reviewer: Adrian Carabineanu (Bucureşti)

##### MSC:

76-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics |

76Mxx | Basic methods in fluid mechanics |