Model Reduction and Neural Networks Open access Peer reviewed

A Graph-based rank-reduced interface preconditioner for the harmonic linearized navier-stokes equations

David A. Cook, Joshua G. Bugel, Joseph W. Nichols

Theoretical and Computational Fluid Dynamics | Jul 8, 2026

Abstract

Abstract Many advanced prediction and analysis tools for hypersonic boundary layer transition---including resolvent and Input/Output (I/O) analysis---rely on solutions of the harmonic, linearized Navier-Stokes equations (H-LNSE), which produce ill-conditioned and highly non-normal discrete systems. To overcome these challenges, we present a graph-based, rank-reduced interface preconditioner (GRIP) for the iterative solution of the H-LNSE, combining ideas from domain decomposition and graph propagation into a single framework. GRIP demonstrates near-linear scaling with respect to both memory and CPU utilization; it is inherently parallel, memory-efficient, physics-informed, and scalable. In testing, we expose a cause of F-GMRES breakdown for hypersonic linear systems and other non-normal operators. GRIP is applied to two- and three-dimensional Mach 6 boundary layer flows over a flat plate, shedding light on the importance of three-dimensional effects in canonical flows. Additionally, GRIP is applied to three-dimensional Mach 6 flow over a cone with a highly swept fin. Analysis of the response at 247 kHz shows amplification of vortical waves along the strong inboard vortex as well as milder amplification along the weaker, outboard vortex.

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Authors

Researchers on this paper

David A. Cook

first | University of Minnesota System | ORCID 0000-0003-2120-3838

Joshua G. Bugel

middle | University of Minnesota System

Joseph W. Nichols

last | University of Minnesota System

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Advanced Numerical Methods in Computational Mathematics Latest Model Reduction and Neural Networks research Lattice Boltzmann Simulation Studies

Citation

BibTeX

@article{Cook2026Graph,
  title = {A Graph-based rank-reduced interface preconditioner for the harmonic linearized navier-stokes equations},
  author = {David A. Cook and Joshua G. Bugel and Joseph W. Nichols},
  journal = {Theoretical and Computational Fluid Dynamics},
  year = {2026},
  doi = {10.1007/s00162-026-00787-z},
  url = {https://doi.org/10.1007/s00162-026-00787-z}
}

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