Relevant bibliographies by topics / High–Order Spectral Methods

Academic literature on the topic 'High–Order Spectral Methods'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "High–Order Spectral Methods"

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Mercader, I., M. Net, and A. Falques. "Spectral methods for high order equations." Computer Methods in Applied Mechanics and Engineering 91, no. 1-3 (October 1991): 1245–51. http://dx.doi.org/10.1016/0045-7825(91)90076-i.

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Vanharen, Julien, Guillaume Puigt, Xavier Vasseur, Jean-François Boussuge, and Pierre Sagaut. "Revisiting the spectral analysis for high-order spectral discontinuous methods." Journal of Computational Physics 337 (May 2017): 379–402. http://dx.doi.org/10.1016/j.jcp.2017.02.043.

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Thalhammer, Mechthild, Marco Caliari, and Christof Neuhauser. "High-order time-splitting Hermite and Fourier spectral methods." Journal of Computational Physics 228, no. 3 (February 2009): 822–32. http://dx.doi.org/10.1016/j.jcp.2008.10.008.

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Guo, Benyu. "Spectral and Spectral Element Methods for High Order Problems with Mixed Boundary Conditions." Journal of Computational Mathematics 32, no. 4 (June 2014): 392–411. http://dx.doi.org/10.4208/jcm.1403-m4373.

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Zhang, Chao, Hanfeng Yao, and Huiyuan Li. "New space–time spectral and structured spectral element methods for high order problems." Journal of Computational and Applied Mathematics 351 (May 2019): 153–66. http://dx.doi.org/10.1016/j.cam.2018.08.038.

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Aleksic, Branislav. "High order spectral symplectic methods for solving PDEs on GPU." Qatar Foundation Annual Research Forum Proceedings, no. 2013 (November 2013): ICTP 043. http://dx.doi.org/10.5339/qfarf.2013.ictp-043.

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Yoon, Hyun C., and Jihoon Kim. "Spectral deferred correction methods for high‐order accuracy in poroelastic problems." International Journal for Numerical and Analytical Methods in Geomechanics 45, no. 18 (October 19, 2021): 2709–31. http://dx.doi.org/10.1002/nag.3283.

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Gray, M. "Reconstruction of Spectra obtained with PYTHEAS through Photometric Methods." International Astronomical Union Colloquium 149 (1995): 311–13. http://dx.doi.org/10.1017/s0252921100023228.

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PYTHEAS is an imaging spectrophotometer giving high spectral and spatial resolutions in joining together several optical concepts (Le Coarer et al 1992, and Georgelin et al. in these Proceedings). It will be shown in this paper that, contrary to other spectrographs using somewhat complex methods of data reduction, the PYTHEAS imaging spectrometer requires simple photometric methods in order to reconstruct the spectra of astrophysical objects.The CCD image of a continuous spectral energy distribution for a permanent gap between the layers of the Fabry-Perot consists in a series of channelled spectra: each elementary beam, spectrally filtered by the FP interferometer and sampled by a microlens in the frame, gives light to the whole surface of the grism which separates the various F-P orders by displaying them in a line on the detector. Each line or channelled spectrum consists of a series of Fabry pupils (spectral elements), each of them containing the luminous flux emitted on a certain wavelength by the object under investigation. After scanning the FP interferometer across its free spectral range, we obtain a series of shifted channelled spectra whose set provides us with a chart showing the photometric values of flux according to the wavelength. Consequently, some forms of calibration (continuum lamp, spectral lamp) allow the reconstruction of the spectra of the astrophysical object through simple photometric measures.
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Bezrukov, Andrei, and Igor Zarubin. "METHODS FOR IMPROVEMENT OF HIGH-RESOLUTION SPECTROMETER CHARACTERISTICS." Interexpo GEO-Siberia 8 (2019): 226–37. http://dx.doi.org/10.33764/2618-981x-2019-8-226-237.

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The present paper demonstrates results of high-resolution spectrometer characteristics improvement methods. Increasing resolution, spectral range extending and illumination efficiency for the spectrometer were investigated. Obtained results will be found useful in atomic spectroscopy applications such as atomic absorption, atomic emission spectroscopy, mass-spectroscopy, chromatography and others. In order to increase spectrometer resolution it was suggested to use higher diffractive grating curvature radius. Experimentally, characteristics of both spectrometer prototypes assembled using diffractive gratings R1000 and R2000 were obtained and compared. New approach for polychromatous displacement was developed in order to extend operational spectrum range. The main feature is single spectrometer entrance slit for both UV and visible range Paschen-Runge polychromatous with beam splitting by coupled flat folding mirrors placed behind slit. Diffractive grating illumination monitor system was designed in order to provide this spectrometer by alignment control for lightning system. New spectrometer “Grand-2” was fabricated. It includes coupled Paschen-Runge polychromators for UV and visible spectral range providing 12 and 30 pm spectral resolution respectively with single entrance slit equipped with diffractive grating illumination monitoring system. This spectrometer can be used for various atomic spectroscopy applications.
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Tang, Tao, Hehu Xie, and Xiaobo Yin. "High-Order Convergence of Spectral Deferred Correction Methods on General Quadrature Nodes." Journal of Scientific Computing 56, no. 1 (October 25, 2012): 1–13. http://dx.doi.org/10.1007/s10915-012-9657-9.

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Dissertations / Theses on the topic "High–Order Spectral Methods"

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Kannan, Ravishekar. "High order spectral volume and spectral difference methods on unstructured grids." [Ames, Iowa : Iowa State University], 2008.

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Vanharen, Julien. "High-order numerical methods for unsteady flows around complex geometries." Phd thesis, Toulouse, INPT, 2017. http://oatao.univ-toulouse.fr/17967/1/vanharen.pdf.

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This work deals with high-order numerical methods for unsteady flows around complex geometries. In order to cope with the low-order industrial Finite Volume Method, the proposed technique consists in computing on structured and unstructured zones with their associated schemes: this is called a hybrid approach. Structured and unstructured meshes are then coupled by a nonconforming grid interface. The latter is analyzed in details with special focus on unsteady flows. It is shown that a dedicated treatment at the interface avoids the reflection of spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. The extension of this hybrid approach to high-order schemes is limited by the efficiency of unstructured high-order schemes in terms of computational time. This is why a new approach is explored: The Spectral Difference Method. A new framework is especially developed to perform the spectral analysis of Spectral Discontinuous Methods. The Spectral Difference Method seems to be a viable alternative in terms of computational time and number of points per wavelength needed for a given application to capture the flow physics.
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Hao, Zhaopeng. "High-order numerical methods for integral fractional Laplacian: algorithm and analysis." Digital WPI, 2020. https://digitalcommons.wpi.edu/etd-dissertations/612.

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The fractional Laplacian is a promising mathematical tool due to its ability to capture the anomalous diffusion and model the complex physical phenomenon with long-range interaction, such as fractional quantum mechanics, image processing, jump process, etc. One of the important applications of fractional Laplacian is a turbulence intermittency model of fractional Navier-Stokes equation which is derived from Boltzmann's theory. However, the efficient computation of this model on bounded domains is challenging as highly accurate and efficient numerical methods are not yet available. The bottleneck for efficient computation lies in the low accuracy and high computational cost of discretizing the fractional Laplacian operator. Although many state-of-the-art numerical methods have been proposed and some progress has been made for the existing numerical methods to achieve quasi-optimal complexity, some issues are still fully unresolved: i) Due to nonlocal nature of the fractional Laplacian, the implementation of the algorithm is still complicated and the computational cost for preparation of algorithms is still high, e.g., as pointed out by Acosta et al \cite{AcostaBB17} 'Over 99\% of the CPU time is devoted to assembly routine' for finite element method; ii) Due to the intrinsic singularity of the fractional Laplacian, the convergence orders in the literature are still unsatisfactory for many applications including turbulence intermittency simulations. To reduce the complexity and computational cost, we consider two numerical methods, finite difference and spectral method with quasi-linear complexity, which are summarized as follows. We develop spectral Galerkin methods to accurately solve the fractional advection-diffusion-reaction equations and apply the method to fractional Navier-Stokes equations. In spectral methods on a ball, the evaluation of fractional Laplacian operator can be straightforward thanks to the pseudo-eigen relation. For general smooth computational domains, we propose the use of spectral methods enriched by singular functions which characterize the inherent boundary singularity of the fractional Laplacian. We develop a simple and easy-to-implement fractional centered difference approximation to the fractional Laplacian on a uniform mesh using generating functions. The weights or coefficients of the fractional centered formula can be readily computed using the fast Fourier transform. Together with singularity subtraction, we propose high-order finite difference methods without any graded mesh. With the use of the presented results, it may be possible to solve fractional Navier-Stokes equations, fractional quantum Schrodinger equations, and stochastic fractional equations with high accuracy. All numerical simulations will be accompanied by stability and convergence analysis.
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Junior, Carlos Breviglieri. "High-order unstructured spectral finite volume method for aerodynamic applications." Instituto Tecnológico de Aeronáutica, 2010. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=1133.

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An implicit finite volume algorithm is developed for higher-order unstructured computation of inviscid compressible flows. The Spectral Finite Volume method is used to achieve high-order spatial discretization of the domain, coupled with a matrix-free LU-SGS algorithm to solve the linear systems arising from implicit time marching of the governing equations, avoiding the explicit storage of the flux Jacobian matrices. A new limiter formulation for the high-order terms of the reconstruction polynomial is introduced. The issue of mesh refinement in accuracy measurements for unstructured meshes is investigated. A straightforward methodology is applied for accuracy assessment of the higher-order unstructured approach based on entropy levels and direct solution error calculation. The accuracy, fast convergence and robustness of the proposed higher-order unstructured solver for different speed regimes are demonstrated via several known test cases from the literature for the 2nd-, 3rd- and 4th-order discretizations. The possibility of reducing the computational cost required for a given level of accuracy using high-order discretization is demonstrated. The main features of the present methodology include the reconstruction algorithm that yields 2nd-, 3rd- and 4th-order spatially accurate schemes, an implicit time march algorithm, high-order domain boundaries representation and a hierarchical moment limiter to treat flow solution discontinuities.
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Lundquist, Tomas. "High order summation-by-parts methods in time and space." Doctoral thesis, Linköpings universitet, Beräkningsmatematik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-126172.

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This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes of high order methods can be applied in a way that satisfies a summation-by-parts rule. These include, but are not limited to, finite difference, spectral and nodal discontinuous Galerkin methods. In the first part of this thesis, the summation-by-parts methodology is extended to the time domain, enabling fully discrete formulations with superior stability properties. The resulting time discretization technique is closely related to fully implicit Runge-Kutta methods, and may alternatively be formulated as either a global method or as a family of multi-stage methods. Both first and second order derivatives in time are considered. In the latter case also including mixed initial and boundary conditions (i.e. conditions involving derivatives in both space and time). The second part of the thesis deals with summation-by-parts discretizations on multi-block and hybrid meshes. A new formulation of general multi-block couplings in several dimensions is presented and analyzed. It collects all multi-block, multi-element and  hybrid summation-by-parts schemes into a single compact framework. The new framework includes a generalized description of non-conforming interfaces based on so called summation-by-parts preserving interpolation operators, for which a new theoretical accuracy result is presented.
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Vadsola, Mayank. "High-Order Spectral Element Method Simulation of Flow Past a 30P30N Three-Element High Lift Wing." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40964.

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The purpose of a multi-element high lift device is to increase lift dramatically while controlling the stall limit. The fluid flow over a multi-element high lift device has been explored widely both experimentally and numerically at high Reynolds numbers (O(10^6 )). The numerical simulations use turbulence models and hence details of the flow are not yet available. Low Reynolds number (O(10^4 )) flows over high lift devices have not been explored until recently. These lower Reynolds number flows have applications in the development of small aerial vehicles. The present work discusses both two-dimensional and three-dimensional direct numer- ical simulations of fluid flow over a 30P30N three-element high lift system using a high-order spectral element method code, Nek5000, that solves the incompressible Navier-Stokes equations. The intricate geometry of the multi-element device poses a challenge for the high-order spectral element method. We study the complex flow physics in the slat cove region and the wake/shear layer interaction over a 30P30N three-element high lift device. The targeted cases are at Reynolds num- bers based on stowed chord lengths (Rec ) of 8.32 × 10^3 , 1.27 × 10^4 , and 1.83 × 10^4 at angle of attack of 4. A critical interval for Rec has previously been found between 1.27 × 10^4 and 1.38 × 10^4 in experiments. This divides the flow into two types: when Rec is below the critical interval, no roll-up is observed in the slat cove and Görtler vortices dominate the slat wake; however when the Rec is above the critical interval, a roll-up is observed in the slat cove and co-existence of streamwise and spanwise vortices is confirmed in the slat wake. We confirm the presence of the critical interval from the simulations performed at three values of Rec . Lift and drag analysis is provided along with pressure coefficient plots for each element of the multi-element airfoil. Different vortical structures are also identified in the transition of flow from two dimensions to three dimensions. The relevant validation is performed with the available experimental data.
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Harris, Robert Evan. "An adaptive quadrature-free implementation of the high-order spectral volume method on unstructured grids." [Ames, Iowa : Iowa State University], 2008.

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Thomas, Gregory Robert. "A combined high-order spectral and boundary integral equation method for modelling wave interactions with submerged bodies." Thesis, Monterey, California. Naval Postgraduate School, 1996. http://hdl.handle.net/10945/8098.

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Thomas, Gregory Robert. "A combined high-order spectral and boundary integral equation method for modelling wave interactions with submerged bodies." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/17432.

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Barnes, Caleb J. "An Implicit High-Order Spectral Difference Method for the Compressible Navier-Stokes Equations Using Adaptive Polynomial Refinement." Wright State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1315591802.

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Books on the topic "High–Order Spectral Methods"

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Hesthaven, Jan S. High-order/spectral methods on unstructured grids. Hampton, VA: ICASE, National Aeronautics and Space Administration, Langley Research Center, 2001.

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Hesthaven, J. S. High-order/spectral methods on unstructured grids. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2001.

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Jameson, Leland. A wavelet-optimized, very high order adaptive grid and order numerical method. Hampton, Va: Langley Research Center, 1996.

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Hesthaven, Jan S., and Einar M. Rønquist, eds. Spectral and High Order Methods for Partial Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15337-2.

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Azaïez, Mejdi, Henda El Fekih, and Jan S. Hesthaven, eds. Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01601-6.

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Bittencourt, Marco L., Ney A. Dumont, and Jan S. Hesthaven, eds. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65870-4.

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Sherwin, Spencer J., David Moxey, Joaquim Peiró, Peter E. Vincent, and Christoph Schwab, eds. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39647-3.

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Kirby, Robert M., Martin Berzins, and Jan S. Hesthaven, eds. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19800-2.

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Cai, Wei. Uniform high order spectral methods for one and two dimensional Euler equations. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1991.

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International Conference on Spectral and High Order Methods (1992 Montpellier, France). Analysis, algorithms, and applications of spectral and high order methods for partial differential equations: Selected papers from the International Conference on Spectral and High Order Methods (ICOSAHOM '92), Le Corum, Montpellier, France, 22-26 June 1992. Amsterdam: North-Holland, 1994.

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Book chapters on the topic "High–Order Spectral Methods"

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Henderson, Ronald D. "Adaptive Spectral Element Methods for Turbulence and Transition." In High-Order Methods for Computational Physics, 225–324. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03882-6_3.

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Hutchinson, Maxwell, Alexander Heinecke, Hans Pabst, Greg Henry, Matteo Parsani, and David Keyes. "Efficiency of High Order Spectral Element Methods on Petascale Architectures." In Lecture Notes in Computer Science, 449–66. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41321-1_23.

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Winters, Andrew R., David A. Kopriva, Gregor J. Gassner, and Florian Hindenlang. "Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier–Stokes Equations." In Efficient High-Order Discretizations for Computational Fluid Dynamics, 117–96. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60610-7_3.

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Beck, A., T. Bolemann, T. Hitz, V. Mayer, and C. D. Munz. "Explicit High-Order Discontinuous Galerkin Spectral Element Methods for LES and DNS." In Lecture Notes in Computational Science and Engineering, 281–96. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22997-3_17.

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Poëtte, G., B. Després, and D. Lucor. "Uncertainty Propagation for Systems of Conservation Laws, High Order Stochastic Spectral Methods." In Lecture Notes in Computational Science and Engineering, 293–305. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15337-2_27.

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Atak, Muhammed, Andrea Beck, Thomas Bolemann, David Flad, Hannes Frank, and Claus-Dieter Munz. "High Fidelity Scale-Resolving Computational Fluid Dynamics Using the High Order Discontinuous Galerkin Spectral Element Method." In High Performance Computing in Science and Engineering ´15, 511–30. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-24633-8_33.

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Parsani, Matteo, Michael Bilka, and Chris Lacor. "Large Eddy Simulation of a Muffler with the High-Order Spectral Difference Method." In Lecture Notes in Computational Science and Engineering, 337–47. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01601-6_27.

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Beck, Andrea, Thomas Bolemann, David Flad, Nico Krais, Jonas Zeifang, and Claus-Dieter Munz. "Application and Development of the High Order Discontinuous Galerkin Spectral Element Method for Compressible Multiscale Flows." In High Performance Computing in Science and Engineering ' 18, 291–307. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13325-2_18.

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Beck, Andrea, Thomas Bolemann, David Flad, Hannes Frank, Nico Krais, Kristina Kukuschkin, Matthias Sonntag, and Claus-Dieter Munz. "Application and Development of the High Order Discontinuous Galerkin Spectral Element Method for Compressible Multiscale Flows." In High Performance Computing in Science and Engineering ' 17, 387–407. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-68394-2_23.

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Shen, Jie, Tao Tang, and Li-Lian Wang. "Higher-Order Differential Equations." In Spectral Methods, 201–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-540-71041-7_6.

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Conference papers on the topic "High–Order Spectral Methods"

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Breviglieri, C., F. M. Moreira, and J. L. F. Azevedo. "HIGH-ORDER SPECTRAL METHODS FOR COMPRESSIBLE FLOWS ON UNSTRUCTURED MESHES." In 10th World Congress on Computational Mechanics. São Paulo: Editora Edgard Blücher, 2014. http://dx.doi.org/10.5151/meceng-wccm2012-18256.

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Abramov, A., A. Sugak, and V. Sugak. "High Order Spectral Estimation Methods in Ground Penetrating Radar Applications." In 2007 International Kharkiv Symposium Physics and Engrg. of Millimeter and Sub-Millimeter Waves (MSMW). IEEE, 2007. http://dx.doi.org/10.1109/msmw.2007.4294838.

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Nastase, Cristian, and Dimitri Mavriplis. "High-Order Discontinuous Galerkin Methods using a Spectral Multigrid Approach." In 43rd AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-1268.

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Cassinelli, Andrea, Francesco Montomoli, Paolo Adami, and Spencer J. Sherwin. "High Fidelity Spectral/hp Element Methods for Turbomachinery." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75733.

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The high order spectral/hp element methods implemented in the software framework Nektar++ are investigated for scale-resolving simulations of LPT profiles. There is a growing demand for high fidelity methods for turbomachinery to move towards numerical “experiments”. The study contributes at building best practices for the use of emerging high fidelity spectral element methods in turbomachinery predictions, with focus on the numerical details that are specific of these classes of methods. For this reason, the T106A cascade is used as a base reference application because of availability of data from previous investigations. The effects of polynomial order (p-refinement), spanwise domain extent and spanwise Fourier planes are considered, looking at flow statistics, convergence and sensitivity of the results. The performance of the high order spectral/hp element method is also assessed through validation against experimental data at moderately high Reynolds number. Thanks to the reduced computational cost, the proposed methods will have a strong impact in turbomachinery, paving the way to its use for design purposes and also allowing for a deeper understanding of the flow physics.
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Jourdan, Eduardo, Fábio Mallaco Moreira, Carlos Breviglieri, André Ribeiro de Barros Aguiar, and João Luiz F. Azevedo. "EVALUATION OF IMPLICIT TIME MARCHING SCHEMES FOR HIGH-ORDER SPECTRAL DIFFERENCE METHODS." In 16th Brazilian Congress of Thermal Sciences and Engineering. ABCM, 2016. http://dx.doi.org/10.26678/abcm.encit2016.cit2016-0154.

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Seriani, Geza, and Enrico Priolo. "High‐order spectral element method for acoustic wave modeling." In SEG Technical Program Expanded Abstracts 1991. Society of Exploration Geophysicists, 1991. http://dx.doi.org/10.1190/1.1888989.

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Seriani, Geza, Enrico Priolo, Jose Carcione, and Enrico Padovani. "High‐order spectral element method for elastic wave modeling." In SEG Technical Program Expanded Abstracts 1992. Society of Exploration Geophysicists, 1992. http://dx.doi.org/10.1190/1.1821973.

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Wang, Z. J., Laiping Zhang, and Yen Liu. "High-Order Spectral Volume Method for 2D Euler Equations." In 16th AIAA Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-3534.

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Wang, Z. J. "High-Order Spectral Volume Method for Benchmark Aeroacoustic Problems." In 41st Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-880.

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Walters, D. Keith, Shanti Bhushan, and Wayne Strasser. "A Wall-Modeled Large Eddy Simulation Method for High-Order Spectral Element Solvers." In ASME 2022 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/fedsm2022-87742.

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Abstract A new method for implementation of wall-modeled large eddy simulation (WMLES) for use with high-order spectral element methods is introduced. Spectral element methods present unique challenges for wall modeling, specifically related to the application of appropriate wall boundary conditions and the specification of modeled fluxes in the near-wall region. The new method addresses these difficulties through the use of an assumed wall function velocity profile in the first layer of near-wall elements, which is used to determine the wall shear stress as well as appropriate pseudo-fluxes to be summed and implemented as source terms at each grid point located in the near-wall elements. Furthermore, the method ensures that the mean velocity field is C1 continuous at the interface between the wall-modeled region and the outer region. Simulations are performed using the spectral element solver Nek5000, and results are compared to high-fidelity DNS data. The test cases considered are fully developed channel flow and flow over a backward-facing step with separation and reattachment. Variations are investigated including different values of the subgrid stress model coefficients for the baseline LES method used. The results show that the new wall function methodology produces results in close agreement with more fully resolved LES for attached channel flow and produces good agreement with field quantities for the backward facing step. The magnitude of wall shear stress in the separated/reattaching flow is underpredicted, and potential reasons for this are discussed. Because WMLES provides a savings in computational cost that scales with Reynolds number, further improvements to the new wall-modeling strategy can potentially lead to significant savings in computational effort for scale-resolving simulations using spectral element numerical methods.
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Reports on the topic "High–Order Spectral Methods"

1

Wang, Z. J. Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids. Office of Scientific and Technical Information (OSTI), December 2012. http://dx.doi.org/10.2172/1056665.

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2

Yue, Dick K. Assimilation of Three-Dimensional Phase-Resolved Wave-Field Data Using an Efficient High-Order Spectral Method. Fort Belvoir, VA: Defense Technical Information Center, August 2001. http://dx.doi.org/10.21236/ada626896.

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3

Lieberman, Evan. Polycrystalline Problems and High-Order Methods. Office of Scientific and Technical Information (OSTI), May 2019. http://dx.doi.org/10.2172/1512723.

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4

Visbal, Miguel R., Scott E. Sherer, and Michael D. White. High-Order Methods For Wave Propagation. Fort Belvoir, VA: Defense Technical Information Center, January 2008. http://dx.doi.org/10.21236/ada475754.

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5

Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, August 2008. http://dx.doi.org/10.21236/ada500484.

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6

Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, March 2013. http://dx.doi.org/10.21236/ada578239.

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7

Shu, Chi-Wang. High Order Numerical Methods for Discontinuous or High Gradient Problems. Fort Belvoir, VA: Defense Technical Information Center, March 1998. http://dx.doi.org/10.21236/ada344382.

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8

Gottlieb, David, and Wai-Sun Don. High Order Accuracy Methods for Supersonic Reactive Flows. Fort Belvoir, VA: Defense Technical Information Center, June 2008. http://dx.doi.org/10.21236/ada483410.

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9

Shu, Chi-Wang. High Order Numerical Methods for Convection Dominated Problems. Fort Belvoir, VA: Defense Technical Information Center, October 2004. http://dx.doi.org/10.21236/ada427595.

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10

Gottlieb, David. High-Order Time-Domain Methods for Maxwells Equations. Fort Belvoir, VA: Defense Technical Information Center, August 2000. http://dx.doi.org/10.21236/ada387163.

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