Dominant balance-based adaptive mesh refinement for incompressible fluid flows

TL;DR

This paper presents a new adaptive mesh refinement method based on dominant balance analysis that automatically identifies critical regions in fluid flow simulations, reducing computational costs while maintaining accuracy.

Contribution

It introduces a fully automated, problem-independent AMR approach using dominant balance analysis and Gaussian mixture models, avoiding heuristic parameters.

Findings

Achieves comparable accuracy to high-resolution grids

Reduces computational costs by up to 70%

Effectively captures complex flow features

Abstract

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions in the equation space. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined parameters, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70%. The validation highlights the method's effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.