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Calcolo

, 55:44 | Cite as

A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity

  • Rim Aldbaissy
  • Frédéric Hecht
  • Gihane Mansour
  • Toni Sayah
Article
  • 242 Downloads

Abstract

In this article, we study the time dependent Boussinesq (buoyancy) model with nonlinear viscosity depending on the temperature. We propose and analyze first and second order numerical schemes based on finite element methods. An optimal a priori error estimate is then derived for each numerical scheme. Numerical experiments are presented that confirm the theoretical accuracy of the discretization.

Keywords

Boussinesq, Buoyancy, Navier–Stokes equations Heat equation Finite element method A priori error estimates 

Mathematics Subject Classification

35Q30 65L60 35Kxx 35B45 

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Copyright information

© Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche 2018

Authors and Affiliations

  • Rim Aldbaissy
    • 1
    • 2
  • Frédéric Hecht
    • 1
  • Gihane Mansour
    • 2
  • Toni Sayah
    • 2
  1. 1.UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis LionsSorbonne UniversitésParisFrance
  2. 2.Laboratoire de Mathétiques et Applications, Unité de recherche Mathématiques et Modélisation, Faculté des SciencesUniversité Saint-JosephBeyrouthLebanon

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