An efficient numerical method for estimating the average free boundary velocity in an inhomogeneous Hele-Shaw problem

TL;DR

This paper introduces a numerical approach to accurately estimate the average free boundary velocity in an inhomogeneous Hele-Shaw problem, demonstrating its effectiveness through tests and examples, and revealing facets in the homogenization limit.

Contribution

A novel numerical method for estimating free boundary velocity in inhomogeneous Hele-Shaw problems with periodic coefficients.

Findings

Method accurately estimates boundary velocity

Numerical evidence of facets in homogenization limit

Validated through tests and examples

Abstract

We develop a numerical method to estimate the average speed of the free boundary in a Hele-Shaw problem with periodic coefficients in both space and time. We test the accuracy of the method and present a few examples. We show numerical evidence of flat parts (facets) on the free boundary in the homogenization limit.