The Hele-Shaw model for the phase field method and the vortex sheet approach

TL;DR

This paper explores the connection between the phase field method and vortex sheet approach within the Hele-Shaw model, aiming to enhance understanding of fluid dynamics phenomena involving pressure, temperature, and volume changes.

Contribution

It introduces a novel relationship between the phase field method and vortex sheet approach applied to the Hele-Shaw model, bridging two computational techniques in fluid dynamics.

Findings

Established a link between phase field and vortex sheet methods for Hele-Shaw flow.

Provided insights into modeling pressure and temperature effects in fluid dynamics.

Proposed a framework for solving complex fluid interface problems.

Abstract

Various thermodynamical phenomena have occurred with change of pressure and temperature, volume. We can choose these parameters but not these constraints, in order to need the thermodynamics with physical properties in the fields of various situations. The Hele-Shaw flow is one of the classical fluid dynamics problems in chemical engineering. Indeed, the Stokes flow is represented as the Stokes equations which is simplified from the famous Navier-Stokes equations. However we have often to deal with the Hele-Shaw flow with the Darcy's law. This law is derived by the Stokes equations. The basic ideas are the executive concepts. Our original work would like to solve the unknown relationship between the phase field method and the vortex sheet approach to the Hele-Shaw model.