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An incompressible smoothed particle hydrodynamics scheme for Newtonian/non‐Newtonian multiphase flows including semi‐analytical solutions for two‐phase inelastic Poiseuille flows
Author(s) -
Xenakis Antonios M.,
Lind Steven J.,
Stansby Peter K.,
Rogers Benedict D.
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4802
Subject(s) - hagen–poiseuille equation , newtonian fluid , mechanics , non newtonian fluid , compressibility , physics , smoothed particle hydrodynamics , generalized newtonian fluid , classical mechanics , flow (mathematics) , viscosity , thermodynamics , shear rate
Summary An incompressible smoothed particle hydrodynamics (ISPH) method is developed for the modeling of multiphase Newtonian and inelastic non‐Newtonian flows at low density ratios. This new method is the multiphase extension of Xenakis et al, J. Non‐Newtonian Fluid Mech., 218, 1‐15, which has been shown to be stable and accurate, with a virtually noise‐free pressure field for single‐phase non‐Newtonian flows. For the validation of the method a semi‐analytical solution of a two‐phase Newtonian/non‐Newtonian (inelastic) Poiseuille flow is derived. The developed method is also compared with the benchmark multiphase case of the Rayleigh Taylor instability and a submarine landslide, thereby demonstrating capability in both Newtonian/Newtonian and Newtonian/non‐Newtonian two‐phase applications. Comparisons with analytical solutions, experimental and previously published results are conducted and show that the proposed methodology can accurately predict the free‐surface and interface profiles of complex incompressible multi‐phase flows at low‐density ratios relevant, for example, to geophysical environmental applications.