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Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics. (English) Zbl 1375.76149

Summary: We present a consistent implicit incompressible smoothed particle hydrodynamics (\(\mathrm I^2\)SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent \(\mathrm I^2\)SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

MSC:

76M28 Particle methods and lattice-gas methods
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