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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Improvement and Verification of Online Cross Section Generation Capability of Griffin for TRISO-fueled Reactors

Griffin, a MOOSE-based reactor multiphysics code jointly developed by Idaho National Laboratory and Argonne National Laboratory under the DOE Office of Nuclear Energy’s NEAMS program, has pursued the development of an online multigroup cross section generation capability for a few years to enable high-fidelity, problem-dependent neutronics analyses of advanced thermal reactors. Recent advancements in Griffin’s online multigroup cross section generation capability have significantly improved the accuracy, robustness, and efficiency of self-shielding calculations for both prismatic and pebble-bed TRISO-fueled reactor applications. Key developments include a unified fuel self-shielding method applicable to both TRISO and annular compact/spherical shell fuel zone geometries; an advanced Dancoff Category-based Equivalence Theory using a bell function for non-fuel resonance treatment, achieving more than an order-of-magnitude speedup compared to the Tone method; an on-the-fly multigroup equivalence approach to mitigate group condensation errors; and a streaming correction method for pebble-bed homogenization. A proof-of-concept demonstration of on-the-fly group condensation with consistent P0 transport correction was also achieved. The method reproduced direct fine-group solutions with excellent accuracy (eigenvalue errors within 10 pcm and pin-power differences within 0.5%), but due to performance limitations of the current fixed-source solver, improvements to solver efficiency will be addressed in future work. Verification tests were performed on graphite-moderated TRISO-fueled two-dimensional core benchmark problems representing gas-cooled microreactors, heat pipe-cooled microreactors, gas-cooled pebble-bed reactors, and fluoride salt-cooled high-temperature reactors. Across all cases, Griffin showed excellent agreement with Serpent2 continuous energy Monte Carlo solutions: eigenvalue errors within 200 pcm, pin-power root-mean-square errors within 2%, and control rod and drum worth errors less than 2%. It should be noted that, for the benchmark problem, cross section generation contributed less than 3% of the total simulation times. These results demonstrate that Griffin’s online cross section generation capability delivers accurate and efficient reactor physics solutions across a wide spectrum of TRISO-fueled advanced reactor designs. With further improvements to the fine-group fixed-source solver and planned extensions to depletion, transients, and coupled neutron–gamma transport, Griffin will be well-positioned to become a powerful and comprehensive tool for advanced reactor analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1974

Vibration and stress analysis of soft-bonded shuttle insulation tiles. Modal analysis with compact widely space stringers

An efficient iterative procedure is described for the vibration and modal stress analysis of reusable surface insulation (RSI) of multi-tiled space shuttle panels. The method, which is quite general, is rapidly convergent and highly useful for this application. A user-oriented computer program based upon this procedure and titled RESIST (REusable Surface Insulation Stresses) has been prepared for the analysis of compact, widely spaced, stringer-stiffened panels. RESIST, which uses finite element methods, obtains three dimensional tile stresses in the isolator, arrestor (if any) and RSI materials. Two dimensional stresses are obtained in the tile coating and the stringer-stiffened primary structure plate. A special feature of the program is that all the usual detailed finite element grid data is generated internally from a minimum of input data. The program can accommodate tile idealizations with up to 850 nodes (2550 degrees-of-freedom) and primary structure idealizations with a maximum of 10,000 degrees-of-freedom. The primary structure vibration capability is achieved through the development of a new rapid eigenvalue program named ALARM (Automatic LArge Reduction of Matrices to tridiagonal form).

Ojalvo, I. U.↗
NASA NTRS1977

A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner

Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.

Watson, W. R.↗
NASA NTRS1990

Dynamic substructuring by the boundary flexibility vector method of component mode synthesis

Component mode synthesis (CMS) is a method of dynamic analysis, for structures having a large number of degrees of freedom (DOF). These structures often required lengthy computer CPU time and large computer memory resources, if solved directly by the finite-element method (FEM). In CMS, the structure is divided into independent components in which the DOF are defined by a set of generalized coordinates defined by displacement shapes. The number of the generalized coordinates are much less than the original number of physical DOF, in the component. The displacement shapes are used to transform the component property matrices and any applied external loads, to a reduced system of coordinates. Reduced system property matrices are assembled, and any type of dynamic analysis is carried out in the reduced coordinate system. Any obtained results are back transformed to the original component coordinate systems. In all conventional methods of CMS, the mode shapes used for components are dynamic mode shapes, supplemented by static deflected shapes. Historically, all the dynamic mode shapes used in conventional CMS are the natural modes (eigenvectors) of components. A new method of CMS, namely the boundary flexibility vector method of CMS, is presented. The method provides for the incorporation of a set of static Ritz vectors, referred to as boundary flexibility vectors, as a replacement and/or supplement to conventional eigenvectors, as displacement shapes for components. The generation of these vectors does not require the solution of a costly eigenvalue problem, as in the case of natural modes in conventional CMS, and hence a substantial saving in CPU time can be achieved. The boundary flexibility vectors are generated from flexibility (or stiffness) properties of components. The formulation presented is for both free and fixed-interface components, and for both the free and forced vibration problems. Free and forced vibration numerical examples are presented to verify the accuracy of the method and the saving in CPU time. Compared to conventional methods of CMS, the results indicate that by using the new method, more accurate results can be obtained with a substantial saving in CPU time.

Abdallah, Ayman Ahmed↗
NASA NTRS1981

Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method

The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.

Hodges, Dewey H.↗
NASA NTRS1992

Collapse analysis of a waffle plate strongback for Space Station Freedom

The structural integrity was studied of the Integrated Equipment Assembly (IEA) Strongback of the SSF for the launch environment. The strongback structure supports the electrical power system for SSF. To achieve minimum launch mass, it is essential that flight structures are designed as light as possible. A nonlinear structural analysis was conducted to determine the collapse load of the structure and the associated factor of safety against the service loads. A modeling technique is provided for simulating the load conditions and the buckling and post buckling (collapse) load is evaluated of the IEA Strongback structure, using the finite element computer code MARC. Two of four strongback panels were modeled and analyzed. The effects were examined of the following factors on the global behavior of the strongback panels: (1) load simplification and simulation; (2) type of support boundary conditions; and (3) the possibility of weight reduction of the original structure. For this purpose, several models of the two panels of the strongback were considered. The stress level and distribution in the panels for launch condition, the Eigenvalue critical buckling load and/or the collapse load were determined.

Monasa, Frank F.↗
NASA NTRS1993

An investigative study of multispectral data compression for remotely-sensed images using vector quantization and difference-mapped shift-coding

A study is conducted to investigate the effects and advantages of data compression techniques on multispectral imagery data acquired by NASA's airborne scanners at the Stennis Space Center. The first technique used was vector quantization. The vector is defined in the multispectral imagery context as an array of pixels from the same location from each channel. The error obtained in substituting the reconstructed images for the original set is compared for different compression ratios. Also, the eigenvalues of the covariance matrix obtained from the reconstructed data set are compared with the eigenvalues of the original set. The effects of varying the size of the vector codebook on the quality of the compression and on subsequent classification are also presented. The output data from the Vector Quantization algorithm was further compressed by a lossless technique called Difference-mapped Shift-extended Huffman coding. The overall compression for 7 channels of data acquired by the Calibrated Airborne Multispectral Scanner (CAMS), with an RMS error of 15.8 pixels was 195:1 (0.41 bpp) and with an RMS error of 3.6 pixels was 18:1 (.447 bpp). The algorithms were implemented in software and interfaced with the help of dedicated image processing boards to an 80386 PC compatible computer. Modules were developed for the task of image compression and image analysis. Also, supporting software to perform image processing for visual display and interpretation of the compressed/classified images was developed.

Jaggi, S.↗
DOE OSTI2024

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1986

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗
DOE OSTI2024

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗
NASA NTRS2003

Algorithmic Enhancements to the VULCAN Navier-Stokes Solver

VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.

Litton, D. K.↗
NASA NTRS1987

A general method for dynamic analysis of structures overview

The presented research deals with the development of a dynamic analysis method for structural systems. The modeling approach is essentially a finite element method in the sense that the structure is divided into n elements. An element is defined as any structural unit whose degree of freedom (dofs) can be categorized as either interface or non-interface dofs. An element could be a fundamental unit such as a rod, a beam, a plate etc., or it could be an entire structural component. Furthermore, the parameters for the element could be distributed or lumped. The choice of elements is totally arbitrary and is a matter of user convenience. In particular, issues of accuracy and convergence do not enter on the level of example that bookkeeping is reduced to a minimum. Each element is modeled using a set of interface constraint modes (ICM) combined with a set of interface restrained normal models (IRNM). The next step is the solution of the system eigenvalue problem. The procedure calls for the sequential solution of a number of small eigenvalue problems based on a truncation principle for IRNM. In addition, the form of these eigenvalue problems is very simple such that an escalator type of eigenvalue problem solver can be used which is extremely cost-effective and fast.

Engels, Remi C.↗
NASA NTRS1976

On a numerical solution of the supersonic panel flutter eigenproblem

An automated digital computer procedure is presented in this paper which enables efficient solution of the eigenvalue problem associated with the supersonic panel flutter phenomena. The step-by-step incremental solution procedure is based on an inverse iteration technique which effectively utilizes solution results from the previous step in determining such results during the current solution step. Also, the computations are limited to the determination of a few specific roots only, which are expected to contain the flutter mode, and this is achieved at each step without having to compute any other root. The structural discretization achieved by the finite-element method yields highly banded stiffness, mass, and aerodynamic matrices; the aerodynamic matrix evaluated by the linearized piston theory is real but unsymmetric in nature. The solution algorithm presented in this paper fully exploits the banded form of the associated matrices, and the resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most efficient and economical when compared to existing procedures of such analysis. Numerical results are presented for a two-dimensional panel flutter problem.

Gupta, K. K.↗
DOE OSTI2024

Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Deployment of neural-network-based neutron microscopic cross sections in the Griffin reactor physics application

The capability to utilize neural networks to predict macroscopic and microscopic cross section parametric spaces has been developed for the Griffin reactor physics application. The LibTorch interface enables Griffin's MOOSE-based materials to interact with LibTorch-trained models, allowing for the evaluation of complex macroscopic or microscopic cross section spaces, which are then used to evaluate the neutronic properties of the Griffin finite element model. This study benchmarks traditional ISOXML-formatted tabulation libraries against neural network-based models for 279 nuclides on 20,160 grid points for zero-dimensional and two-dimensional reactor models. Benchmark metrics include the fundamental mode eigenvalue, fission and absorption rates, and various temperature coefficients of reactivity (isothermal, fuel, and moderator). From the perspective of storage space, the complete set of LibTorch models uses 11 MB on disk, compared to the 10 GB for the ISOXML multigroup library that covers the same grid space. For the two-dimensional performance case considered in Griffin, the Torch model uses 97% less RAM than the reference ISOXML dataset while runtime increases by a factor of 3 when using the LibTorch model compared to the ISOXML dataset with multi-linear interpolation. The LibTorch model consistently yields errors within 0.01% for most analyzed quantities except for the temperature coefficients of reactivity where the maximum discrepancies are up to 0.3 $\frac{pcm}{K}$. Due to the neural network attempting to best predict quantities with no regard for a positive or negative bias for any given quantity, predictions may experience random fluctuations, resulting in both positive and negative errors. Future work will entail both depletion and coupled transient analysis to determine the predictive capabilities of Griffin with neural network-based cross sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRSDate not supplied

High-Fidelity Flight Dynamic Analysis of Transonic Truss-Braced Wing

This paper presents a high-fidelity flight dynamic analysis of the Mach 0.8 Transonic Truss-Braced Wing (TTBW). Unsteady RANS CFD simulations of the Mach 0.8 TTBW in pitch, plunge, roll, and yaw oscillations are conducted in FUN3D. The time-domain data are transformed into the frequency-domain data by Fourier series. Transfer functions of the dynamic stability derivatives are then estimated by a frequency-domain re- gression. The dynamic stability derivatives with respect to the angle of attack are determined by the regression of the unsteady aerodynamic coefficients for the plunge motion. The dynamic stability derivatives with re- spect to the pitch rate are determined by the regression of the differential unsteady aerodynamic coefficients for the pitch motion upon the removal of the angle of attack contribution by the plunge motion. Similarly, dynamic stability derivatives with respect to the angle of sideslip, roll rate, and yaw rates are determined from the frequency domain regression. The longitudinal and lateral-direction flight dynamic models of the Mach 0.8 TTBW are constructed from these dynamic stability derivatives. The eigenvalues of the aircraft modes are analyzed to determine the vehicle stability.

Aircraft Stability and Control↗
NASA NTRSDate not supplied

Stability Analysis of the Flow over a Swept Forward-Facing Step using PIV Base Flowsin a Non-Orthogonal Coordinate System

Understanding the flow of a crossflow-vortex-dominated boundary layer over a forward-facing step excrescence is necessary in order to mitigate an early transition scenario on the wings and tail of commercial aircraft. By performing BiGlobal stability analysis on the flowfield measured with high-resolution, stereographic Particle Image Velocimetry (PIV), previous work has shown that a family of unstable disturbances exists in the direct downstream vicinity of a supercritical, forward-facing step. The goal of the present paper is to improve the previously used stability approach on two fronts: 1) the stability problem is formulated in a non-orthogonal coordinate system and 2) the contribution of the out-of-plane base-flow derivatives is accounted for locally. The resulting eigen solutions feature significantly stronger growth rates and eigenfunctions that are localized above regions of reverse flow. The changes in the problem formulation furthermore establish a significant improvement in the comparison of the stability solutions with the results from the Spectral Proper Orthogonal Decomposition (SPOD) of a time-resolved measurement of the perturbation content. A large destabilizing effect by the out-of-plane base-flow derivatives is determined to be justified, despite the assumption that these derivatives are small, because the effect can be reconstructed upon using an eigenvalue-correction formula that assumes the responsible terms are infinitesimally small. The unstable perturbation mechanisms are demonstrated to have a convective nature by assessing the relation between the frequency and the out-of-plane wavenumber, which indicates that their group speed does not approach zero. The last 2 facts, that 1) the perturbations are convective and 2) that the out-of-plane base-flow-derivative terms are small, remove any qualitative suspicions that the perturbation problem is not conducive to parabolization. This opens the path to analyzing this problem with a plane-marching approach.

Boundary- Layer Transition↗