8 papers
A Cartesian Grid Method for Advection-Diffusion Equations with Robin Boundary Conditions on Moving Domains
Han Zhou, Yoichiro Mori, Lingxing Yao
The paper presents a Cartesian grid finite‑difference method for solving advection‑diffusion equations with Robin boundary conditions on domains that move over time, using an inter…
Modeling and Simulation of Open Membranes in Stokes Flow with Mixed-Dimensional Coupling
Han Zhou, Yuan-Nan Young, Yoichiro Mori
The paper introduces a mathematical and computational framework that couples three‑dimensional Stokes flow, a two‑dimensional lipid bilayer membrane, and its one‑dimensional free e…
On the global asymptotic stability for the 3D Peskin Problem at critical regularity
Eduardo GarcÃa-Juárez, Susanna V. Haziot, Po-Chun Kuo +2
The paper proves that a three‑dimensional elastic membrane immersed in a Stokes fluid (the Peskin problem) has globally well‑posed solutions that become smooth instantly and conver…
Stability and equilibria of a compressible elastic membrane in Stokes flow
Sho Kawakami, Han Zhou, Po-Chun Kuo +2
We formulate a continuum model for a compressible lipid-bilayer membrane immersed in Stokes flow, replacing exact local area inextensibility by conservation of an areal phospholipi…
A Cartesian grid-based boundary integral method for moving interface problems
Han Zhou, Shuwang Li, Wenjun Ying
This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stef…
A Correction Function-based KFBI Method for Brinkman Interface Problems
Han Zhou, Wenjun Ying
In this work, we propose a correction-function-based kernel-free boundary integral (CF-KFBI) method for solving Stokes- and Brinkman-type interface problems. We begin by recasting…