Recursive one-way Navier-Stokes equations with PSE-like cost

Zhu, Min; Towne, Aaron

doi:10.1016/j.jcp.2022.111744

Cited by 7 publications

(4 citation statements)

References 58 publications

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“…To obtain a system of linear hyperbolic equations of type ( 1), second derivatives in x and cross derivatives in Navier-Stokes equations are neglected, as it is generally the case in One-Way approaches [28,29]. We next proceed as explained in Section 2 by choosing the privileged direction x, consider the equations in the harmonic regime and then discretize them in the transverse direction y.…”

Section: Governing Equationsmentioning

confidence: 99%

Domain decomposition method based on One-Way approaches for sound propagation in a partially lined duct

Ruello,

Rudel,

Pernet

et al. 2024

Wave Motion

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Section: Governing Equationsmentioning

confidence: 99%

Domain decomposition method based on One-Way approaches for sound propagation in a partially lined duct

Ruello,

Rudel,

Pernet

et al. 2024

Wave Motion

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“…In the PSE formalism, when chemical reactions are included among the modeling equations, it is possible that efficient preconditioners can be constructed based on the block structure of the equations. Another problem for which economic preconditioners may be constructed is the one-way Navier Stokes (OWNS) equations which were proposed by Towne and coworkers [17][18][19]. The OWNS solves two major shortcomings of the PSE formalism, as they are both well-posed and include the interaction between different instability modes.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

“…The other drawback of the PSE formalism is that it can only capture the evolution of individual modes and fails to correctly capture the interaction of multiple instability modes correctly [15]. The above shortcoming led to the development of more rigorous parabolization techniques that resolve both issues but are computationally more cumbersome [17][18][19]. Despite these drawbacks, the PSE method has been extended to compressible and hypersonic flows [20][21][22], curvilinear coordinates [23] and three-dimensional boundary layers [4,24], nonequilibrium thermo-chemical interactions and reacting flows [25][26][27][28], and surface movement [27].…”

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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“…The present OWNS computations were performed on a single node due to limitations of the employed PARDISO solver. Future work includes MPI-enabled PARDISO and/or adopting the more efficient solution strategy of [80] to fully exploit the unique and powerful features of the OWNS methodology, including 3D input-output analysis.…”

mentioning

confidence: 99%

Assessment of Linear Methods for Analysis of Boundary Layer Instabilities on a Finned Cone at Mach 6

Araya

Bitter

Wheaton

et al. 2022

AIAA AVIATION 2022 Forum

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Boundary-layer instabilities for a finned cone at Mach = 6, Re = 8.4 × 10 6 [ −1 ], and zero incidence angle are examined using linear stability methods of varying fidelity and maturity, following earlier analysis presented in [1]. The geometry and laminar flow conditions correspond to experiments conducted at the Boeing Air Force Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. Where possible, a common mean flow is utilized among the stability computations, and comparisons are made along the acreage of the cone where transition is first observed in the experiment. Stability results utilizing Linear Stability Theory (LST), planar Parabolized Stability Equations (planar-PSE), One-Way Navier Stokes (OWNS), forced direct numerical simulation (DNS), and Adaptive Mesh Refinement Wavepacket Tracking (AMR-WPT) are presented. A dominant three-dimensional vortex instability occurring at ≈ 250 kHz is identified that correlates well with experimental measurements of transition onset. With the exception of LST, all of the higher-fidelity linear methods considered in this work were consistent in predicting the initial growth and general structure of the vortex instability as it evolved downstream. Some of the challenges, opportunities, and development needs of the stability methods considered are discussed.

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Recursive one-way Navier-Stokes equations with PSE-like cost

Cited by 7 publications

References 58 publications

Domain decomposition method based on One-Way approaches for sound propagation in a partially lined duct

Domain decomposition method based on One-Way approaches for sound propagation in a partially lined duct

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

Assessment of Linear Methods for Analysis of Boundary Layer Instabilities on a Finned Cone at Mach 6

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