Energy inequalities and outflow boundary conditions for the navier-stokes equations

Norikazu Saito, Yoshiki Sugitani, Guanyu Zhou

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Artificial boundary conditions play important roles in numerical simulation of real-world flow problems. A typical example is a class of outflow boundary conditions for blood flow simulations in large arteries. The common outflow boundary conditions are a prescribed constant pressure or traction,a prescribed velocity profiles,and a free-traction (do-nothing) conditions. However,the flow distribution and pressure field are unknown and cannot be prescribed at the outflow boundary in many simulations. Moreover,with those boundary conditions,we are unable to obtain energy inequalities. This disadvantage may cause numerical instability in unstationary 3D simulations. In this paper,we examine some outflow boundary conditions for the Navier-Stokes equations from the viewpoint of energy inequalities. Further,we propose an energy-preserving unilateral condition and review mathematical results including the well-posedness,variational inequality formulations,and finite element approximations.

Original languageEnglish
Title of host publicationModeling and Simulation in Science, Engineering and Technology
PublisherSpringer Basel
Pages307-317
Number of pages11
DOIs
Publication statusPublished - 2016
Externally publishedYes

Publication series

NameModeling and Simulation in Science, Engineering and Technology
ISSN (Print)2164-3679
ISSN (Electronic)2164-3725

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Fluid Flow and Transfer Processes
  • Computational Mathematics

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