Resolving singular forces in cavity flow: Multiscale modeling from atoms to millimeters

TL;DR

This paper introduces a multiscale modeling approach that combines atomistic and continuum methods to accurately resolve stress singularities in cavity flow, achieving significant computational speedup and revealing universal and atomistic effects.

Contribution

A novel multiscale method that retains atomistic detail in key regions to resolve singularities in cavity flow, bridging microscopic and macroscopic scales.

Findings

Resolved stress singularities in cavity flow for the first time.

Achieved over fourteen orders of magnitude speedup compared to pure atomistic simulations.

Discovered universal dependence on Reynolds number and atomistic effects related to wall velocity.

Abstract

A multiscale approach for fluid flow is developed that retains an atomistic description in key regions. The method is applied to a classic problem where all scales contribute: The force on a moving wall bounding a fluid-filled cavity. Continuum equations predict an infinite force due to stress singularities. Following the stress over more than six decades in length in systems with characteristic scales of millimeters and milliseconds allows us to resolve the singularities and determine the force for the first time. The speedup over pure atomistic calculations is more than fourteen orders of magnitude. We find a universal dependence on the macroscopic Reynolds number, and large atomistic effects that depend on wall velocity and interactions.