Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit

摘要

The paper presents various formulations of characteristics-based schemes in the framework of the artificialcompressibilitymethod 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 densityflows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. Theconservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shownthat in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressibleflows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant densityflows. The characteristics-based schemes are combined with second and third-order interpolation for increasing thecomputational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flowsreveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergencebehavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of thisstudy.