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arXiv · 2607.02880

A Geometric Local Parameterization Method for Generalized Hele-Shaw Free Boundary Problems with Source Terms

Zengyan Zhang·Wenrui Hao·John Harlim
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Abstract

We develop a meshfree numerical framework for Hele--Shaw free boundary problems with surface tension and source terms based on geometric local parameterization and boundary integral methods. By decomposing the pressure into a particular solution and a harmonic component, the problem is reformulated into a boundary-only system, avoiding volumetric meshing of the evolving domain. For general source terms, we propose an eigenfunction-based approximation on a fixed domain and establish error estimates for both the truncation and coefficient approximation. Numerical experiments verify the accuracy and convergence of the proposed method, and an application to a tumor growth model demonstrates its effectiveness for coupled moving-boundary problems.

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Zengyan Zhang, Wenrui Hao, John Harlim. 2026-07-03. A Geometric Local Parameterization Method for Generalized Hele-Shaw Free Boundary Problems with Source Terms. https://arxiv.org/abs/2607.02880

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