Adaptive Mesh Refinement (AMR)

The Adaptive Mesh Refinement (AMR) technique provides a powerful tool for high-fidelity, high-resolution simulations. To capture complex processes in simulations, a high grid resolution is needed to resolve small structures. However, these fine structures may not be present everywhere, therefore 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 AMR method, which increases the grid resolution in regions of interest as needed during the simulation while leaving general estimates in other regions.

Based on AMReX, we have developed a block-structured AMR (BSAMR) framework on the multi-level collocated grid. This framework utilizes the level set (LS) method for simulating two-phase flows and the distributed Lagrange multiplier method for fluid-structure interaction (FSI) problems. Both the subcycling and non-subcycling methods are implemented for time advancement in this unified framework. We have used AMR to simulate a wide range of fluid mechanics problems, including the dam breaking, wave energy converters, and biomimetics.

Schematic of the sub-steps in the level-by-level advancement method for a three-level grid. Left: the subcycling method. Right: the non-subcycling method. The sub-steps are represented by the circled numbers.
Schematic of the Block Structured Adaptive Mesh Refinement (BSAMR) method.
Schematic of the sub-steps in the level-by-level advancement method for a three-level grid. Left: the subcycling method. Right: the non-subcycling method. The sub-steps are represented by the circled numbers.
Evolution of the air-water interface for the Rayleigh--Taylor instability problem with three-level subcycling.
The black line represents the air-water interface. The green and blue lines represent the patches on level 1 and level 2, respectively.