ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

A discrete kinetic approximation for the incompressible Navier-Stokes equations

Carfora, Maria Francescaa1 and Natalini, Robertoa2

a1 Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via P. Castellino, 111, 80131, Napoli, Italia. f.carfora@iac.cnr.it

a2 Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 Roma, Italia. r.natalini@iac.cnr.it

Abstract

In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H-theorem. Numerical tests are performed to investigate their convergence and accuracy.

(Received May 24 2006)

(Revised April 19 2007)

(Online publication January 12 2008)

Key Words:

  • Incompressible fluids;
  • kinetic schemes;
  • BGK models;
  • finite difference schemes.

Mathematics Subject Classification:

  • 65M06;
  • 76M20;
  • 76R
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