Delaunay Refinement Algorithm for Particle Finite Element Method in Free Surface Flows

Основные понятия

Proposing a Delaunay refinement strategy for mesh adaptation in the Particle Finite Element Method to improve stability and accuracy in modeling free surface flows.

Аннотация

This paper introduces a Delaunay refinement algorithm for the Particle Finite Element Method (PFEM) applied to free surface flows. The PFEM uses a Lagrangian approach with particles defining the fluid and a triangular mesh connecting them. Mesh adaptation is crucial for locating the free surface accurately. The proposed Delaunay refinement strategy ensures stable and smooth free surface geometries. The PFEM models a single fluid domain but requires boundary conditions for free surfaces and internal bubbles. A multi-point constraint approach is suggested to enforce global incompressibility of empty bubbles. The methodology, mesh adaptation, boundary conditions, and verification tests are detailed.

Статистика

"The mesh generation community has acquired a lot of experience and understanding about mesh adaptation approaches with guarantees of quality on the final mesh."
"The Delaunay refinement strategy allows to insert and remove nodes while gradually improving mesh quality."
"The mesh is of poor quality has two consequences: solving the equations on a quality mesh is important for obtaining a good accuracy."
"The detection of the fluid domain actually depends on mesh quality."
"The approach used here is based on a Delaunay refinement strategy, allowing to insert and remove nodes while gradually improving mesh quality."

Цитаты

"The mesh generation community has acquired a lot of experience and understanding about mesh adaptation approaches with guarantees of quality on the final mesh."
"The Delaunay refinement strategy allows to insert and remove nodes while gradually improving mesh quality."
"The detection of the fluid domain actually depends on mesh quality."

Ключевые выводы из

A Delaunay Refinement Algorithm for the Particle Finite Element Method applied to Free Surface Flows

by Thomas Leyss... в arxiv.org 03-28-2024

https://arxiv.org/pdf/2403.18416.pdf

Дополнительные вопросы

How does the Delaunay refinement strategy compare to other mesh adaptation approaches?

The Delaunay refinement strategy stands out among other mesh adaptation approaches due to its ability to ensure high-quality mesh with theoretical guarantees. Unlike some other methods that may rely on ad-hoc criteria for mesh adaptation, the Delaunay refinement strategy leverages the well-established Delaunay triangulation to insert and remove nodes while gradually improving mesh quality. This approach is based on Chew's algorithm, which has been proven to maintain mesh quality by avoiding the creation of elements with small angles. By enforcing a high-quality Delaunay mesh at all times and refining it based on a user-defined size field, the Delaunay refinement strategy provides stability and accuracy in capturing complex geometries, such as free surface flows.

What are the implications of enforcing global incompressibility of empty bubbles in free surface flows?

Enforcing global incompressibility of empty bubbles in free surface flows has significant implications for accurately modeling bubbly flows. By imposing a multi-point constraint approach to maintain incompressibility within the bubbles, the model ensures that the volume of the bubbles remains constant despite the dynamic changes in the surrounding fluid. This approach allows for the accurate representation of two-fluid systems with large density differences, such as water and air, while only modeling the heavier fluid. By incorporating the incompressibility constraint, the model can capture the behavior of bubbles within the fluid domain, preventing them from deflating or disappearing due to pressure imbalances. This ensures a more realistic simulation of bubbly flows and enhances the overall fidelity of the model.

How can the proposed multi-point constraint approach enhance the accuracy of modeling bubbly flows?

The proposed multi-point constraint approach enhances the accuracy of modeling bubbly flows by addressing the incompressibility of empty bubbles within the fluid domain. By introducing a pressure term that enforces incompressibility and incorporating an incompressibility constraint for each bubble, the model ensures that the volume of the bubbles remains constant and accurately represents the behavior of two-fluid systems. This approach allows for the realistic simulation of bubbly flows involving bubbles encapsulated within the fluid, maintaining their integrity and preventing them from collapsing or disappearing. By enforcing global incompressibility through multi-point constraints, the model can accurately capture the dynamics of bubbly flows with large density differences, improving the overall accuracy and reliability of the simulation results.