Mass Conservative Reduced Order Modeling of a Free Boundary Osmotic Cell Swelling Problem

TL;DR

This paper develops a mass-conservative reduced order model for a free boundary osmotic cell swelling problem, ensuring accurate and efficient simulations while preserving key physical properties.

Contribution

It introduces a novel reduced basis approach with empirical interpolation that maintains mass conservation in free boundary problems.

Findings

Reduced order model accurately predicts cell swelling dynamics.

Mass conservation is exactly preserved in the reduced model.

Numerical experiments demonstrate computational efficiency.

Abstract

We consider model order reduction for a free boundary problem of an osmotic cell that is parameterized by material parameters as well as the initial shape of the cell. Our approach is based on an Arbitrary-Lagrangian-Eulerian description of the model that is discretized by a mass-conservative finite element scheme. Using reduced basis techniques and empirical interpolation, we construct a parameterized reduced order model in which the mass conservation property of the full-order model is exactly preserved. Numerical experiments are provided that highlight the performance of the resulting reduced order model.