Navier-Stokes Equations in Planar Domains

Nonfiction, Science & Nature, Mathematics, Differential Equations, Applied
Cover of the book Navier-Stokes Equations in Planar Domains by Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov, World Scientific Publishing Company
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Author: Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov ISBN: 9781783263011
Publisher: World Scientific Publishing Company Publication: March 7, 2013
Imprint: ICP Language: English
Author: Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov
ISBN: 9781783263011
Publisher: World Scientific Publishing Company
Publication: March 7, 2013
Imprint: ICP
Language: English

This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.

A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.

This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics.

Contents:

  • Basic Theory:

    • Introduction
    • Existence and Uniqueness of Smooth Solutions
    • Estimates for Smooth Solutions
    • Extension of the Solution Operator
    • Measures as Initial Data
    • Asymptotic Behavior for Large Time
    • Some Theorems from Functional Analysis
  • Approximate Solutions:

    • Introduction
    • Notation
    • Finite Difference Approximation to Second-Order Boundary-Value Problems
    • From Hermitian Derivative to the Compact Discrete Biharmonic Operator
    • Polynomial Approach to the Discrete Biharmonic Operator
    • Compact Approximation of the Navier–Stokes Equations in Streamfunction Formulation
    • Fully Discrete Approximation of the Navier–Stokes Equations
    • Numerical Simulations of the Driven Cavity Problem

Readership: Graduate students and researchers in applied mathematics (particularly computational fluid dynamics), partial differential equations, and mathematical physics (specifically nonlinear evolution equations).
Key Features:

  • Provides an up-to-date account of recent developments in vorticity theory
  • Presents comprehensive treatment of viscous flow problems in flat domains
  • Addresses the classical problem: How rapidly do rotating flows evolve in time?
  • Includes theoretical and numerical methods
  • Presents state-of-the-art streamfunction formalism (theoretical and numerical)
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.

A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.

This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics.

Contents:

Readership: Graduate students and researchers in applied mathematics (particularly computational fluid dynamics), partial differential equations, and mathematical physics (specifically nonlinear evolution equations).
Key Features:

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