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<p>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 hypersonic H-LNSE, combining ideas from domain decomposition and graph propagation into a single framework. Along an application-driven Reynolds-number/frequency scaling path, in which the physically relevant disturbance frequency and mesh requirements increase with unit Reynolds number, GRIP exhibits favorable empirical cost growth, with near-linear CPU-time and memory growth relative to the resulting discrete problem size over the tested range. GRIP 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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

摘要

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 hypersonic H-LNSE, combining ideas from domain decomposition and graph propagation into a single framework. Along an application-driven Reynolds-number/frequency scaling path, in which the physically relevant disturbance frequency and mesh requirements increase with unit Reynolds number, GRIP exhibits favorable empirical cost growth, with near-linear CPU-time and memory growth relative to the resulting discrete problem size over the tested range. GRIP 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.