Dominant balance-based adaptive mesh refinement for incompressible fluid flows

Kumar, Gaurav; Nair, Aditya G.

doi:10.1016/j.jcp.2025.114522

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

Journal Article · Wed Nov 26 00:00:00 EST 2025 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2025.114522· OSTI ID:3025291

Kumar, Gaurav ^[1]; ^[1]

Univ. of Nevada, Reno, NV (United States)

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 within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and 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 wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Nevada, Reno, NV (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0022945

OSTI ID:: 3025291

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 547; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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71 CLASSICAL AND QUANTUM MECHANICS
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97 MATHEMATICS AND COMPUTING
Adaptive mesh refinement
Dominant balance analysis
Incompressible flows

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

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