Adaptive Time Stepping for Vesicle Suspensions

TL;DR

This paper introduces an adaptive, high-order accurate time-stepping scheme for simulating vesicle suspensions in Stokesian fluids, balancing computational efficiency with spectral accuracy.

Contribution

It presents a semi-implicit spectral deferred correction scheme with approximations tailored for vesicle flows, enabling automatic step size selection and high-order accuracy.

Findings

Scheme achieves spectral accuracy in space.

Enables automatic adaptive time stepping.

Validated on various vesicle flow scenarios.

Abstract

We present an adaptive arbitrary-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximate implicit spectral deferred correction (SDC) method. Applying a textbook fully implicit SDC scheme to vesicle flows is prohibitively expensive. For this reason we introduce several approximations. Our scheme is based on a semi-implicit linearized low-order time stepping method. (Our discretization is spectrally accurate in space.) We also use invariant properties of vesicle flows, constant area and boundary length in two dimensions, to reduce the computational cost of error estimation for adaptive time stepping. We present results in two dimensions for single-vesicle flows, constricted geometry flows, converging flows, and flows in a Couette apparatus. We experimentally demonstrate that the proposed scheme enables automatic selection of the step size and high-order accuracy.