Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit - Shapiro, Evgeniy; Drikakis, Dimitris (Elsevier, 2005)
The paper presents various formulations of characteristics-based schemes in the framework of the artiﬁcialcompressibility 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.