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 artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density flows, where variables reconstruction leads a single formulation, case variable density flows three different can be obtained henceforth labeled as: transport, conservative and hybrid schemes. scheme results pseudo-compressibility terms (multi-species) reconstruction. It is shown that limit constant density, transport becomes (original) but lead new variant are combined with second third-order interpolation increasing computational accuracy locally at cell faces control volume. Numerical experiments reveal all result same flow solution, they exhibit convergence behavior. multigrid implementation numerical studies presented Part II this study.