Simulation of thin film flows with a moving mesh mixed finite element method

TL;DR

This paper introduces an efficient mixed finite element method with moving mesh refinement for simulating thin film flows, improving accuracy and reducing computational costs compared to fixed mesh approaches.

Contribution

The paper develops a novel moving mesh mixed finite element method for fourth-order thin film equations, incorporating adaptive monitor functions and harmonic mappings.

Findings

Accurately captures overshoot and downshoot structures.

Reduces computational cost compared to fixed mesh methods.

Demonstrates high accuracy and efficiency through numerical tests.

Abstract

We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To achieve a high quality mesh, we adopt an adaptive monitor function and smooth it based on a diffusive mechanism. A variety of numerical tests are performed to demonstrate the accuracy and efficiency of the method. The moving mesh refinement accurately resolves the overshoot and downshoot structures and reduces the computational cost in comparison to numerical simulations using a fixed mesh.