The Voronoi Implicit Interface Method for computing multiphase physics.

Area of Science:

• Computational physics and fluid dynamics.
• Numerical analysis and scientific computing.

Background:

• Tracking multiple interacting and evolving regions (phases) with complex physics, jump conditions, and boundary constraints is computationally challenging.
• Existing methods often struggle with topological changes, multiple junctions, and high-order accuracy.

Purpose of the Study:

• To introduce a novel numerical framework, the Voronoi Implicit Interface Method (VIIM), for tracking multiple interacting and evolving phases.
• To demonstrate the method's capability in handling complex physics, topological changes, and high-order accuracy.

Main Methods:

• The Voronoi Implicit Interface Method (VIIM) uses a single function on a fixed Eulerian mesh to represent all phases simultaneously.
• The method naturally handles topological changes, multiple junctions (triple points, quadruple points), and triple lines in 2D and 3D.
• It achieves first-order accuracy at junction points/lines and arbitrarily high-order accuracy elsewhere.

Main Results:

• The VIIM successfully tracks tens of thousands of interfaces and separate phases in 2D and 3D.
• Demonstrated accuracy through convergence tests and application to geometric flows.
• Successfully predicted von Neumann's law for multiphase curvature flow and showed robustness under complex fluid flow with surface tension and shearing forces.

Conclusions:

• The Voronoi Implicit Interface Method provides a robust and accurate framework for simulating multiphase systems with complex physics and topology.
• The method's ability to handle topological changes naturally and achieve high-order accuracy makes it suitable for advanced scientific simulations.
• VIIM shows significant potential for applications in fluid dynamics, material science, and other fields involving multiphase phenomena.