Boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method

TL;DR

This paper analyzes the boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method, identifying key parameters for stability and minimal velocity error in moving boundary simulations.

Contribution

It introduces a critical parameter for stability and finds an optimal acceleration parameter that minimizes velocity error regardless of boundary details.

Findings

Identifies a critical parameter for numerical stability.

Determines an optimal acceleration parameter for minimal velocity error.

Provides guidelines for stable and accurate moving boundary simulations.

Abstract

The multi-direct-forcing immersed boundary method allows for a small velocity error of the no-slip condition in moving-particle problems but suffers from numerical instability if simulation parameters are not carefully chosen. This study investigates the boundary-velocity error and numerical stability of the accelerated multi-direct-forcing immersed boundary method. An analysis of the discretized equations of body motion in moving boundary problems identifies a critical parameter that solely determines the numerical stability for the body motion. Additionally, numerical simulations reveal the optimal acceleration parameter that minimizes the velocity error of the no-slip condition and is independent of details of the boundary discretisation, the boundary shape, and spatial dimensionality. This study provides a guideline for establishing numerically stable simulations of moving boundary problems at optimal boundary-velocity error.