Projection Method for Solving Stokes Flow

TL;DR

This paper introduces a new projection method for solving Stokes flow that decouples pressure and velocity variables without requiring constant viscosity, reducing computational costs and enabling applications like red blood cell modeling.

Contribution

A novel decoupling approach for Stokes flow that overcomes viscosity limitations present in existing methods.

Findings

The new method reduces computational complexity.

It allows decoupling with spatially variable viscosity.

Potential applications in biological cell modeling.

Abstract

Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the numerical solution can be obtained with significantly less computation cost than when compared to solving a fully coupled system. Two existing methods for numerically solving Stokes Flow are explored: One where the variables can be decoupled and one where they cannot. The existing decoupling method the limitation that the viscosity must be spatially constant. A new method is introduced where the variables are decoupled without the viscosity limitation. This has potential applications in the modeling of red blood cells as vesicles to assist in storage techniques that do not require extreme temperatures, such as those needed for cyropreservation.