TY - JOUR
T1 - Artificial compressibility, characteristics-based schemes for variable-density, incompressible, multispecies flows
T2 - Part II. Multigrid implementation and numerical tests
AU - Shapiro, Evgeniy
AU - Drikakis, Dimitris
N1 - Funding Information:
The financial support from the UK’s Engineering and Physical Sciences Research Council (GR/S13668) is greatly acknowledged.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2005/12/10
Y1 - 2005/12/10
N2 - 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.
AB - 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.
KW - Artificial compressibility
KW - Characteristics-based schemes
KW - Euler equations
KW - High-resolution schemes
KW - Microfluidics
KW - Mixing layer
KW - Multigrid
KW - Navier-Stokes equations
KW - Variable-density flows
UR - http://www.scopus.com/inward/record.url?scp=23944471716&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2005.05.002
DO - 10.1016/j.jcp.2005.05.002
M3 - Article
AN - SCOPUS:23944471716
SN - 0021-9991
VL - 210
SP - 608
EP - 631
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -