An Eulerian Meshless Method for Two-phase Flows with Embedded Geometries

TL;DR

This paper introduces a new meshless Eulerian method for simulating two-phase flows with complex embedded geometries, enabling accurate boundary condition enforcement and stable interface tracking without traditional meshing.

Contribution

The novel method combines meshless GFDM with direct boundary condition imposition at embedded geometries, improving accuracy and flexibility over conventional immersed boundary techniques.

Findings

Validated with benchmark tests for two-phase flows

Demonstrated capability with embedded boundary geometries

Achieved stable and accurate interface tracking

Abstract

We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked using a volume fraction function. The volume fraction is advected using a method based on the minimisation of a directional flux-based error. For stability, the advection terms are discretised using upwinding schemes. In the vicinity of the embedded geometries, the signed distance function is used to populate the surface of the geometries to generate a body-conforming point cloud. Consequently, the points on the boundaries participate directly in the discretisation, unlike conventional immersed-boundary methods where they are either used to calculate momentum deficit (for example, continuous forcing) or conservation losses (for example, cut-cell methods). The boundary conditions are, therefore, directly imposed at these points on the embedded geometries, opening up the possibility for a discretisation that is body-conforming and spatially varying in resolution, while retaining the consistency of the scheme. We present benchmark test cases that validate the method for two-phase flows, flows with embedded boundaries and a combination of both.