Matrix methods for input-output analysis of 2D and 3D hypersonic flows

Cook, David A.; Knutson, Anthony; Nichols, Joseph W.; Candler, Graham V.

doi:10.2514/6.2020-1820

Cited by 5 publications

(2 citation statements)

References 18 publications

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“…An ideal preconditioner is easy to calculate and provides a good approximation of the inverse and it is also computationally cheap to apply. Recently, it was noted in the boundary layer research community by [18,66] that without a good preconditioner, general iterative methods indeed perform very poorly.…”

Section: Introductionmentioning

confidence: 99%

Reused LU factorization as a preconditioner for efficient solution of the Parabolized Stability Equations

Szabó

Paál

2023

Preprint

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The parabolized stability equation (PSE) is a widely used, efficient method to calculate the evolution of streamwise traveling instabilities in spatially developing, weakly nonparallel flows. Although the PSE method is very economical, computational time can be significant due to the repeated solution of linear systems of equations in each marching step. The linear systems of equations are typically solved by LU factorization due to the moderate size and the sparsity of the coefficient matrices. In this paper, instead of repeated calculation of the LU factorization, a single LU factorization is calculated in each marching step, and used as a preconditioner for an iterative solver. Numerical experiments are conducted on the incompressible PSE, nonlinear PSE (NLPSE) with explicit discretization of the nonlinear terms, and NLPSE with implicit treatment of the nonlinearities. It is shown that the time spent on the solution of the linear systems of equations was reduced by a factor of 2.5, 4.5-7.5, and 20-60 for the three cases, respectively. The methodology can be generalized to the compressible PSE equations, and extended to similar boundary layer stability problems, or slowly varying parabolic partial differential equations.

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Section: Introductionmentioning

confidence: 99%

Reused LU factorization as a preconditioner for efficient solution of the Parabolized Stability Equations

Szabó

Paál

2023

Preprint

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“…Recently, a new technique referred to as resolvent or input/output analysis has been introduced that combines the linear receptivity and instability problem via optimization techniques, such as singular value decomposition (SVD), to determine inflow disturbances that lead to maximal amplification [12]. These global analyses have been historically tractable for simple geometries at low-speeds [13], but their extension to high-speed flows have gained recent attention [14,15]. While promising results have been shown, their application to practical, in-flight geometries would involve complex algorithms and large-scale computing.…”

Section: Introductionmentioning

confidence: 99%

Input/Output Analysis of Hypersonic Boundary Layers using the One-Way Navier-Stokes (OWNS) Equations

Kamal

Rigas

Lakebrink

et al. 2021

Aiaa Aviation 2021 Forum

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Accurate prediction of linear amplification of disturbances in hypersonic boundary layers is computationally challenging. While direct numerical simulations (DNS) and global analysis can be used to compute optimal (worst-case) disturbances and forced responses, their large computational expense render these tools less practical for large design parameter spaces. At the same time, parabolized stability equations can be unreliable for problems involving multimodal and non-modal interactions. To bridge this gap, we apply an approximate fast marching technique, the One-Way Navier-Stokes (OWNS) Equations, in iterative fashion to solve for optimal disturbances. OWNS approximates a rigorous parabolization of the equations of motion by removing disturbances with upstream group velocity using a higher-order recursive filter. Using OWNS, we aim to characterize disturbances of flat-plate hypersonic boundary layers over a range of Mach numbers, and find optimal disturbances under different cost functions that define corresponding receptivity problems. The calculation of optimal disturbances reveals multi-modal transition scenarios depending on the spatial support, frequency, and physical nature of the external disturbances.

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Global receptivity analysis: physically realizable input–output analysis

2023

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In the context of transition analysis, linear input–output analysis determines the worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations of a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.

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Matrix methods for input-output analysis of 2D and 3D hypersonic flows

Cited by 5 publications

References 18 publications

Reused LU factorization as a preconditioner for efficient solution of the Parabolized Stability Equations

Reused LU factorization as a preconditioner for efficient solution of the Parabolized Stability Equations

Input/Output Analysis of Hypersonic Boundary Layers using the One-Way Navier-Stokes (OWNS) Equations

Global receptivity analysis: physically realizable input–output analysis

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