Error Estimation for Adaptive Mesh Refinement in Droplet Simulations

TL;DR

This paper introduces a flux-based error estimation method for adaptive mesh refinement in droplet simulations, improving interface accuracy by refining the mesh based on error estimates derived from smooth interface gradients.

Contribution

It develops a novel flux-based error estimation approach integrated with adaptive mesh refinement for droplet interface simulation using a mixed finite element method.

Findings

Enhanced accuracy of droplet interface capture

Effective mesh refinement driven by error estimates

Improved curvature calculation in droplet simulations

Abstract

We present a one-dimensional shear force driven droplet formation model with a flux-based error estimation. The presented model is derived using asymptotic expansion and a front-tracking method to simulate the droplet interface. The model is then discretized using the Galerkin finite element method in the mixed form. However, the jumps in the solution gradients are discontinuous and can grow faster due to the highly convective pinch-off process. This leads to an erroneous droplet interface and incorrect curvature. Therefore, the mesh must be sufficiently refined to capture the interface accurately. The mixed form of the governing equation naturally provides smooth interface gradients that can be used to compute the error estimate. The computed error estimate is then used to drive the adaptive mesh refinement algorithm.