Arbitrary slip length for fluid-solid interface of arbitrary geometry in smoothed particle dynamics

TL;DR

This paper introduces a method to model arbitrary slip lengths at fluid-solid interfaces in smoothed particle dynamics, enabling accurate simulation of complex geometries with adjustable slip conditions.

Contribution

It develops two approaches for calculating artificial boundary velocities to implement arbitrary slip lengths in particle-based fluid simulations, applicable to complex geometries.

Findings

Slip length can be precisely controlled in simulations.

Method accurately reproduces expected slip behaviors in various flows.

Applicable to both steady and transient flow simulations.

Abstract

We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity at quasi-steady state near the interface, an arbitrary slip length $b$ can be specified and correspondingly, an artificial velocity for every boundary particle can be calculated. Therefore, $b$ as an input parameter affects the calculation of dissipative and random forces near the interface. For $b \to 0$, the no-slip is recovered while for $b \to \infty$, the free-slip is achieved. Technically, we devise two different approaches to calculate the artificial velocity of any boundary particle. The first has a succinct principle and is competent for simple geometries, while the second is subtle and affordable for complex geometries. Slip lengths in simulations for both steady and transient flows coincide with the expected ones. As demonstration, we apply the two approaches extensively to simulate curvy channel flows, dynamics of an ellipsoid in pipe flow and flows within complex microvessels, where desired slip lengths at fluid-solid interfaces are prescribed. The proposed methodology may apply equally well to other particle methods such as dissipative particle dynamics and moving particle semi-implicit methods.