High-order adaptive time stepping for vesicle suspensions with viscosity contrast

TL;DR

This paper introduces a high-order adaptive time stepping scheme for simulating vesicle suspensions with viscosity contrast, improving accuracy and efficiency in complex biological fluid dynamics.

Contribution

It develops a spectral deferred correction (SDC) based high-order method with adaptive error control for vesicle suspension simulations.

Findings

Method accurately handles tumbling and tank-treading vesicles.

Automatically achieves user-prescribed tolerance over long simulations.

Demonstrates improved stability and precision in complex suspensions.

Abstract

We construct a high-order adaptive time stepping scheme for vesicle suspensions with viscosity contrast. The high-order accuracy is achieved using a spectral deferred correction (SDC) method, and adaptivity is achieved by estimating the local truncation error with the numerical error of physically constant values. Numerical examples demonstrate that our method can handle suspensions with vesicles that are tumbling, tank-treading, or both. Moreover, we demonstrate that a user-prescribed tolerance can be automatically achieved for simulations with long time horizons.