TY - JOUR
T1 - Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit
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 various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.
AB - The paper presents various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.
KW - Artificial compressibility
KW - Characteristics-based schemes
KW - Euler equations
KW - High-resolution schemes
KW - Navier-Stokes equations
KW - Variable density flows
UR - http://www.scopus.com/inward/record.url?scp=23944513362&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2005.05.001
DO - 10.1016/j.jcp.2005.05.001
M3 - Article
AN - SCOPUS:23944513362
SN - 0021-9991
VL - 210
SP - 584
EP - 607
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -