Navier-Stokes Equations In Planar Domains, 1st Edition

  • Published By: Imperial College Press
  • ISBN-10: 1848162766
  • ISBN-13: 9781848162761
  • DDC: 532.052015
  • Grade Level Range: College Freshman - College Senior
  • 316 Pages | eBook
  • Original Copyright 2013 | Published/Released January 2015
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Basic Theory.
2: Introduction.
3: Existence and Uniqueness of Smooth Solutions.
4: Estimates for Smooth Solutions.
5: Extension of the Solution Operator.
6: Measures as Initial Data.
7: Asymptotic Behavior for Large Time.
8: Appendix A: Some Theorems from Functional Analysis.
9: Approximate Solutions.
10: Introduction.
11: Notation.
12: Finite Difference Approximation to Second-Order Boundary-Value Problems.
13: From Hermitian Derivative to the Compact Discrete Biharmonic Operator.
14: Polynomial Approach to the Discrete Biharmonic Operator.
15: Compact Approximation of the Navier–Stokes Equations in Streamfunction Formulation.
16: Appendix B: Eigenfunction Approach for Uxxt − Uxxxx = f (x, t).
17: Fully Discrete Approximation of the Navier–Stokes Equations.
18: Numerical Simulations of the Driven Cavity Problem.