Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations

ISBN-13: 9783519027232 / Angielski / Miękka / 1997 / 308 str.

Andreas Prohl;Andreas Prohl

Opis

The numerical treatment of the evolutionary incompressible Navier-Stokes equations, which determine many practicaIly relevant fluid flows, is an area of considerable interest for industrial as weIl as scientific applications. Im portant for drawing furt her conclusions for the behavior of certain flows in diverse disciplines such as (astro-)physics, engineering, meteorology, oceanog raphy, or biology is a reliable, robust and efficient numerical model. The goal of computing highly complex flows requires the development of sophisticated algorithms. In general, numerical schemes which do not cause high computa tional cost, often suffer from stability or reliability problems and vice versa. So, it demands a numerical and physical a-priori knowledge from the user in order to select the "best fitting algorithm" for a particular problem under consideration. The use of knowledge about physical phenomena appearing in a specific problem aIlows the relaxation of some robustness-conditions that otherwise need to be imposed on the numerical scheme in order to ensure reliability with respect to the convergence behavior. To this end, this leads to permittance of numerical models simulating continuous flows which do not satisfy severe stability restrictions that lead to robust schemes, with the advantage of lower computational costs necessary to obtain the same accu racy. A major part of this book is devoted to such schemes that are of great importance: classical projection methods 01 high er order and nonstationary quasi-compressibility methods.

Spis treści

Introduction - Preliminareis - Stationary Quasi-Compressibility Methods: The Penalty Method and the Pressure Stabilization Method - Nonstationary Quasi-Compressibility Methods - Mixed Quasi-Compressibility Methods - The Projection Scheme of Chorin - The Projection Scheme of Van Kan - Two Modified Chorin Schemes - Multi-Component Schemes - Time Discretization on Time-Grids with Structure from Euler to Revised Projection Schemes

Blurb

Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. "... this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics." J.-L.Guermond. Mathematical Reviews, Ann Arbor