Numerical Methods for Fluids, Part 3
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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Numerical analysis > Numerical Methods for Fluids, Part 3: Volume 9(Volume 9 Handbook of Numerical Analysis)
Numerical Methods for Fluids, Part 3: Volume 9(Volume 9 Handbook of Numerical Analysis)

Numerical Methods for Fluids, Part 3: Volume 9(Volume 9 Handbook of Numerical Analysis)


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About the Book

Due to their modularity the methods described in this article are relatively easy to implement - as is demonstrated by the fact that several practitioners in various institutions have been able to use them ab initio for the solution of complicated flow (and other) problems.

Table of Contents:
Chapter I The Navier-Stokes equations for incompressible viscous fluids: derivation of the Navier-Stokes equations for viscous fluids; initial and boundary conditions; a stream function-vorticity formulation of the Navier-Stokes equations; a brief introduction to Sobolev spaces; variational formulations of the Navier-Stokes equations; a short review of mathematical results for the Navier-Stokes equations. Chapter II A family of operator splitting methods for initial value problems - application to the Navier-Stokes equations: a family of initial value problems; the Peaceman-Rachford method; the Douglas-Rachford method; A-scheme; application to the Navier-Stokes equations. Chapter III Iterative solution of the advection-diffusion subproblems: classical and variational formulations of the advection-diffusion subproblems associated with the operator splitting schemes; linear variational problems in Hilbert spaces; variational methods for the solution of the advection-diffusion problems (13.1) and (13.2); conjugate gradient methods for the solution of minimization problems in Hilbert spaces; least-squares solution of linear and nonlinear problems in Hilbert spaces; least-squares/conjugate gradient solution of problems (13.1) and (13.2). Chapter IV Iterative solution of the Stokes subproblems: mathematical properties of the generalized Stokes problem (GS)1; gradient methods for the Stokes problem; conjugate gradient methods for the Stokes problem (GS)1; iterative solution of the generalized Stokes problem (GS)2; on artificial compressibility methods and further comments. Chapter V Finite element approximation of the Navier-Stokes equations: solution of the Stokes problem with periodic boundary conditions; a Fourier analysis of the numerical instability mechanism; finite element implementation of the scheme (11.5)-(11.8); on the numerical solution of the discrete subproblems. Chapter VI Treatment of the advection by a wave-like equation method and by backward methods of characteristics: more on operator-splitting methods; a wave-like equation method for solving the Navier-Stokes equations; solution of the Navier-Stokes equations by backward methods of characteristics; on the treatment of the advection by upwinding. Chapter VII On L2-projection methods for the numerical treatment of the incompressibility: combining L2-projection methods with operator-splitting schemes la Peaceman-Rachford and Douglas-Rachford, and with the scheme; combining L2-projection methods with operator splitting schemes la Marchuk-Yanenko; numerical experiments. Chapter VIII Fictitious domain methods for incompressible viscous flow - application to particulate flow. Chapter X Complements - from stream function-vorticity to flow control.

Review :
"The book is a remarkable sample of in-depth surveys, which include the most recent trends in mathematical finance…. Reflecting the state of the art in mathematical finance, this handbook is a useful guide in this area for both academics and practitioners."--reviewed in Mathematical Reviews


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Product Details
  • ISBN-13: 9780444512246
  • Publisher: Elsevier Science & Technology
  • Publisher Imprint: Elsevier Science Ltd
  • Language: English
  • Sub Title: Volume 9
  • ISBN-10: 0444512241
  • Publisher Date: 25 Jul 2003
  • Binding: Hardback
  • Series Title: Volume 9 Handbook of Numerical Analysis


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