Artificial compressibility, characteristics-based schemes for variable-density, incompressible, multispecies flows: part II. multigrid implementation and numerical tests

Evgeniy Shapiro, Dimitris Drikakis

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

The paper presents an investigation of the accuracy and efficiency of artificial compressibility, characteristics-based (CB) schemes for variable-density incompressible flows. The CB schemes have been implemented in conjunction with a multigrid method for accelerating numerical convergence and a fourth-order, explicit Runge–Kutta method for the integration of the governing equations in time. The implementation of the CB schemes is obtained in conjunction with first-, second- and third-order interpolation formulas for calculating the variables at the cell faces of the computational volume. The accuracy and efficiency of the schemes are examined against analytical and experimental results for diffusion broadening in two- and three-dimensional microfluidic channels, a problem that has motivated the development of the present methods. Moreover, unsteady, inviscid simulations have been performed for variable-density mixing layer. The computations revealed that accuracy and efficiency depend on the CB scheme design. The best multigrid convergence rates were exhibited by the conservative CB scheme, which is obtained by the fully conservative formulation of the variable-density, incompressible equations.
Original languageEnglish
Pages (from-to)608-631
Number of pages24
JournalJournal of Computational Physics
Volume210
Issue number2
DOIs
Publication statusPublished - 10 Dec 2005

Keywords

  • variable-density flows
  • artificial compressibility
  • characteristics-based schemes
  • multigrid
  • high-resolution schemes
  • microfluidics
  • mixing layers
  • Euler equations
  • Navier–Stokes equations

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