[Paper Review] Numerical Simulations of the Two-phase flow and Fluid-Structure Interaction Problems with Adaptive Mesh Refinement

Yadong Zeng|arXiv (Cornell University)|Jun 1, 2023

Computational Fluid Dynamics and Aerodynamics4 citations

TL;DR

This paper presents a novel block-structured adaptive mesh refinement (BSAMR) framework for simulating two-phase flows and fluid-structure interaction using a level set method on a collocated grid. It unifies subcycling and non-subcycling approaches, enforces divergence-free flow via synchronization operations, and achieves accurate interface resolution with strong momentum and energy conservation.

ABSTRACT

Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high grid resolution is usually needed. However, one does not need or maybe cannot afford a fine grid of uniformly high resolution across the whole domain. The need to resolve local fine features can be addressed by the adaptive mesh refinement (AMR) method, which increases the grid resolution in regions of interest as needed during the simulation while leaving general estimates in other regions. In this work, we propose a block-structured adaptive mesh refinement (BSAMR) framework to simulate two-phase flows using the level set (LS) function with both the subcycling and non-subcycling methods on a collocated grid. To the best of our knowledge, this is the first framework that unifies the subcycling and non-subcycling methods to simulate two-phase flows. The use of the collocated grid is also the first among the two-phase BSAMR framework, which significantly simplifies the implementation of multi-level differential operators and interpolation schemes. We design the synchronization operations, including the averaging, refluxing, and synchronization projection, which ensures that the flow field is divergence-free on the multi-level grid. It is shown that the present multi-level scheme can accurately resolve the interfaces of the two-phase flows with gravitational and surface tension effects while having good momentum and energy conservation.

Motivation & Objective

• To address the computational inefficiency of uniform high-resolution grids in two-phase flow and fluid-structure interaction simulations.
• To develop a block-structured adaptive mesh refinement (BSAMR) framework that dynamically refines regions of interest while maintaining accuracy.
• To unify subcycling and non-subcycling time integration methods within a single two-phase flow framework for improved efficiency and stability.
• To implement a collocated grid scheme that simplifies multi-level differential operators and interpolation in AMR contexts.
• To ensure global divergence-free flow fields across multiple refinement levels using synchronization operations like averaging, refluxing, and projection.

Proposed method

• Adopting a block-structured adaptive mesh refinement (BSAMR) framework to allow local grid refinement in regions with complex flow features.
• Using the level set (LS) function to implicitly track the interface between two immiscible fluids with surface tension and gravity effects.
• Implementing both subcycling and non-subcycling time integration schemes to balance computational efficiency and temporal accuracy.
• Employing a collocated grid arrangement for velocity and pressure variables to simplify the implementation of multi-level operators and interpolation.
• Designing synchronization operations—averaging, refluxing, and projection—between refinement levels to maintain a divergence-free velocity field.
• Applying conservative interpolation and restriction operators to transfer data across refinement levels while preserving mass, momentum, and energy conservation.

Experimental results

Research questions

• RQ1 How can a unified framework be developed to support both subcycling and non-subcycling time integration in two-phase flow simulations using adaptive mesh refinement?
• RQ2 What are the key challenges in enforcing a divergence-free velocity field across multiple refinement levels in a block-structured AMR context?
• RQ3 How does the use of a collocated grid in a two-phase BSAMR framework affect the accuracy and stability of interface tracking and fluid dynamics resolution?
• RQ4 To what extent does the proposed synchronization strategy preserve momentum and energy conservation in multi-level two-phase flow simulations?
• RQ5 Can the framework accurately resolve complex interfacial dynamics, including surface tension and gravitational effects, with localized high resolution?

Key findings

• The proposed BSAMR framework successfully unifies subcycling and non-subcycling methods for two-phase flow simulations, enabling efficient and stable time integration.
• The use of a collocated grid simplifies the implementation of multi-level differential operators and interpolation schemes, reducing algorithmic complexity.
• Synchronization operations—including averaging, refluxing, and projection—effectively maintain a divergence-free velocity field across all refinement levels.
• The method achieves accurate resolution of fluid interfaces under surface tension and gravity, with minimal spurious currents and high geometric fidelity.
• The scheme demonstrates strong conservation of momentum and energy, as evidenced by numerical stability and bounded energy errors over time.
• The framework enables high-resolution capture of local flow features without uniform refinement, significantly reducing computational cost while preserving accuracy.