Multiscale modelling couples patches of two-layer thin fluid flow

TL;DR

This paper extends the multiscale gap-tooth scheme to simulate nonlinear two-layer thin fluid flows efficiently by coupling microscale simulations with macroscale models, validated through eigenvalue analysis and numerical experiments.

Contribution

It develops a two-layer microscale simulator within the gap-tooth framework for nonlinear fluid flow, ensuring stability and computational efficiency.

Findings

The scheme accurately reproduces fluid flow dynamics.

Eigenvalue analysis confirms stability of the microscale model.

Numerical simulations demonstrate computational savings.

Abstract

The multiscale gap-tooth scheme uses a given microscale simulator of complicated physical processes to enable macroscale simulations by computing only only small sparse patches. This article develops the gap-tooth scheme to the case of nonlinear microscale simulations of thin fluid flow. The microscale simulator is derived by artificially assuming the fluid film flow having two artificial layers but no distinguishing physical feature. Centre manifold theory assures that there exists a slow manifold in the two-layer fluid film flow. Eigenvalue analysis confirms the stability of the microscale simulator. This article uses the gap-tooth scheme to simulate the two-layer fluid film flow. Coupling conditions are developed by approximating the values at the edges of patches by neighbouring macroscale values. Numerical eigenvalue analysis suggests that the gap-tooth scheme with the developed two-layer microscale simulator empowers feasible computation of large scale simulations of fluid film flows. We also implement numerical simulations of the fluid film flow by the gap-tooth scheme. Comparison between a gap-tooth simulation and a microscale simulation over the whole domain demonstrates that the gap-tooth scheme feasibly computes fluid film flow dynamics with computational savings.