Relevant bibliographies by topics / High-order discretization methods

Academic literature on the topic 'High-order discretization methods'

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Published: 14 March 2023
Last updated: 25 May 2024

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Journal articles on the topic "High-order discretization methods"

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Gottlieb, Sigal, Chi-Wang Shu, and Eitan Tadmor. "Strong Stability-Preserving High-Order Time Discretization Methods." SIAM Review 43, no. 1 (January 2001): 89–112. http://dx.doi.org/10.1137/s003614450036757x.

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Takács, Bálint, and Yiannis Hadjimichael. "High order discretization methods for spatial-dependent epidemic models." Mathematics and Computers in Simulation 198 (August 2022): 211–36. http://dx.doi.org/10.1016/j.matcom.2022.02.021.

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Filbet, Francis, and Charles Prouveur. "High order time discretization for backward semi-Lagrangian methods." Journal of Computational and Applied Mathematics 303 (September 2016): 171–88. http://dx.doi.org/10.1016/j.cam.2016.01.024.

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Bassi, Francesco, Lorenzo Botti, and Alessandro Colombo. "Agglomeration-based physical frame dG discretizations: An attempt to be mesh free." Mathematical Models and Methods in Applied Sciences 24, no. 08 (May 4, 2014): 1495–539. http://dx.doi.org/10.1142/s0218202514400028.

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In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.
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Chen, Minghua, and Weihua Deng. "Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators." Communications in Computational Physics 16, no. 2 (August 2014): 516–40. http://dx.doi.org/10.4208/cicp.120713.280214a.

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AbstractHigh order discretization schemes play more important role in fractional operators than classical ones. This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones; but for fractional operators the stencils for high order schemes and low order ones are the same. Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved. Using the fractional linear multistep methods, Lubich obtains thev-th order (v <6) approximations of theα-th derivative (α >0) or integral (α <0) [Lubich, SIAM J. Math. Anal., 17, 704-719, 1986], because of the stability issue the obtained scheme can not be directly applied to the space fractional operator withαЄ (1,2) for time dependent problem. By weighting and shifting Lubich’s 2nd order discretization scheme, in [Chen & Deng, SINUM, arXiv:1304.7425] we derive a series of effective high order discretizations for space fractional derivative, called WSLD operators there. As the sequel of the previous work, we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations. In particular, we prove that the obtained 4th order approximations are effective for space fractional derivatives. And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.
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Bose, Mahua, and Kalyani Mali. "High Order Time Series Forecasting using Fuzzy Discretization." International Journal of Fuzzy System Applications 5, no. 4 (October 2016): 147–64. http://dx.doi.org/10.4018/ijfsa.2016100107.

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In recent years, various methods for forecasting fuzzy time series have been presented in different areas, such as stock price, enrollments, weather, production etc. It is observed that in most of the cases, static length of intervals/equal length of interval has been used. Length of the interval has significant role on forecasting accuracy. The objective of this present study is to incorporate the idea of fuzzy discretization into interval creation and examine the effect of positional information of elements within a group or interval to the forecast. This idea outperforms the existing high order forecast methods using fixed interval. Experiments are carried on three datasets including Lahi production data, enrollment data and rainfall data which deal with a lot of uncertainty.
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Yi, Tae-Hyeong, and Francis X. Giraldo. "Vertical Discretization for a Nonhydrostatic Atmospheric Model Based on High-Order Spectral Elements." Monthly Weather Review 148, no. 1 (December 27, 2019): 415–36. http://dx.doi.org/10.1175/mwr-d-18-0283.1.

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Abstract This study addresses the treatment of vertical discretization for a high-order, spectral element model of a nonhydrostatic atmosphere in which the governing equations of the model are separated into horizontal and vertical components by introducing a coordinate transformation, so that one can use different orders and types of approximations in both directions. The vertical terms of the decoupled governing equations are discretized using finite elements based on either Lagrange or basis-spline polynomial functions in the sigma coordinate, while maintaining the high-order spectral elements for the discretization of the horizontal terms. This leads to the fact that the high-order model of spectral elements with a nonuniform grid, interpolated within an element, can be easily accommodated with existing physical parameterizations. Idealized tests are performed to compare the accuracy and efficiency of the vertical discretization methods, in addition to the central finite differences, with those of the standard high-order spectral element approach. Our results show, through all the test cases, that the finite element with the cubic basis-spline function is more accurate than the other vertical discretization methods at moderate computational cost. Furthermore, grid dependency studies in the tests with and without orography indicate that the convergence rate of the vertical discretization methods is lower than the expected level of discretization accuracy, especially in the Schär mountain test, which yields approximately first-order convergence.
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Darrigrand, E., L. Gatard, and K. Mer-Nkonga. "High order boundary integral methods forMaxwell's equations using Microlocal Discretization and Fast Multipole Methods." PAMM 7, no. 1 (December 2007): 1022705–6. http://dx.doi.org/10.1002/pamm.200700332.

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May, Georg, Koen Devesse, Ajay Rangarajan, and Thierry Magin. "A Hybridized Discontinuous Galerkin Solver for High-Speed Compressible Flow." Aerospace 8, no. 11 (October 28, 2021): 322. http://dx.doi.org/10.3390/aerospace8110322.

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We present a high-order consistent compressible flow solver, based on a hybridized discontinuous Galerkin (HDG) discretization, for applications covering subsonic to hypersonic flow. In the context of high-order discretization, this broad range of applications presents unique difficulty, especially at the high-Mach number end. For instance, if a high-order discretization is to efficiently resolve shock and shear layers, it is imperative to use adaptive methods. Furthermore, high-Enthalpy flow requires non-trivial physical modeling. The aim of the present paper is to present the key enabling technologies. We discuss efficient discretization methods, including anisotropic metric-based adaptation, as well as the implementation of flexible modeling using object-oriented programming and algorithmic differentiation. We present initial verification and validation test cases focusing on external aerodynamics.
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Chen, Jing-Bo. "Modeling the scalar wave equation with Nyström methods." GEOPHYSICS 71, no. 5 (September 2006): T151—T158. http://dx.doi.org/10.1190/1.2335505.

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High-accuracy numerical schemes for modeling of the scalar wave equation based on Nyström methods are developed in this paper. Space is discretized by using the pseudospectral algorithm. For the time discretization, Nyström methods are used. A fourth-order symplectic Nyström method with pseudospectral spatial discretization is presented. This scheme is compared with a commonly used second-order scheme and a fourth-order nonsymplectic Nyström method. For a typical time-step size, the second-order scheme exhibits spatial dispersion errors for long-time simulations, while both fourth-order schemes do not suffer from these errors. Numerical comparisons show that the fourth-order symplectic algorithm is more accurate than the fourth-order nonsymplectic one. The capability of the symplectic Nyström method in approximately preserving the discrete energy for long-time simulations is also demonstrated.
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Dissertations / Theses on the topic "High-order discretization methods"

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Tam, Anita W. "High-order spatial discretization methods for the shallow water equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58942.pdf.

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Botti, Michele. "Advanced polyhedral discretization methods for poromechanical modelling." Thesis, Montpellier, 2018. http://www.theses.fr/2018MONTS041/document.

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Dans cette thèse, on s’intéresse à de nouveaux schémas de discrétisation afin de résoudre les équations couplées de la poroélasticité et nous présentons des résultats analytiques et numériques concernant des problèmes issus de la poromécanique. Nous proposons de résoudre ces problèmes en utilisant les méthodes Hybrid High-Order (HHO), une nouvelle classe de méthodes de discrétisation polyédriques d’ordre arbitraire. Cette thèse a été conjointement financée par le Bureau de Recherches Géologiques et Minières (BRGM) et le LabEx NUMEV. Le couplage entre l’écoulement souterrain et la déformation géomécanique est un sujet de recherche crucial pour les deux institutions de cofinancement
In this manuscript we focus on novel discretization schemes for solving the coupled equations of poroelasticity and we present analytical and numerical results for poromechanics problems relevant to geoscience applications. We propose to solve these problems using Hybrid High-Order (HHO) methods, a new class of nonconforming high-order methods supporting general polyhedral meshes. This Ph.D. thesis was conjointly founded by the Bureau de recherches géologiques et minières (BRGM) and LabEx NUMEV. The coupling between subsurface flow and geomechanical deformation is a crucial research topic for both cofunding institutions
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Karouma, Abdulrahman. "A Class of Contractivity Preserving Hermite-Birkhoff-Taylor High Order Time Discretization Methods." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32403.

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In this thesis, we study the contractivity preserving, high order, time discretization methods for solving non-stiff ordinary differential equations. We construct a class of one-step, explicit, contractivity preserving, multi-stage, multi-derivative, Hermite-Birkhoff-Taylor methods of order p=5,6, ..., 15, that we denote by CPHBT, with nonnegative coefficients by casting s-stage Runge-Kutta methods of order 4 and 5 with Taylor methods of order p-3 and p-4, respectively. The constructed CPHBT methods are implemented using an efficient variable step algorithm and are compared to other well-known methods on a variety of initial value problems. The results show that CPHBT methods have larger regions of absolute stability, require less function evaluations and hence they require less CPU time to achieve the same accuracy requirements as other methods in the literature. Also, we show that the contractivity preserving property of CPHBT is very efficient in suppressing the effect of the propagation of discretization errors when a long-term integration of a standard N-body problem is considered. The formulae of 49 CPHBT methods of various orders are provided in Butcher form.
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Kress, Wendy. "High Order Finite Difference Methods in Space and Time." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3559.

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Nissen, Anna. "High Order Finite Difference Methods with Artificial Boundary Treatment in Quantum Dynamics." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-159856.

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The investigation of the dynamics of chemical reactions, both from the theoretical and experimental side, has drawn an increasing interest since Ahmed H. Zewail was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry. On the experimental side, new techniques such as femtosecond lasers and attosecond lasers enable laser control of chemical reactions. Numerical simulations serve as a valuable complement to experimental techniques, not only for validation of experimental results, but also for simulation of processes that cannot be investigated through experiments. With increasing computer capacity, more and more physical phenomena fall within the range of what is possible to simulate. Also, the development of new, efficient numerical methods further increases the possibilities. The focus of this thesis is twofold; numerical methods for chemical reactions including dissociative states and methods that can deal with coexistence of spatial regions with very different physical properties. Dissociative chemical reactions are reactions where molecules break up into smaller components. The dissociation can occur spontaneously, e.g. by radioactive decay, or be induced by adding energy to the system, e.g. in terms of a laser field. Quantities of interest can for instance be the reaction probabilities of possible chemical reactions. This thesis discusses a boundary treatment model based on the perfectly matched layer (PML) approach to accurately describe dynamics of chemical reactions including dissociative states. The limitations of the method are investigated and errors introduced by the PML are quantified. The ability of a numerical method to adapt to different scales is important in the study of more complex chemical systems. One application of interest is long-range molecules, where the atoms are affected by chemical attractive forces that lead to fast movement in the region where they are close to each other and exhibits a relative motion of the atoms that is very slow in the long-range region. A numerical method that allows for spatial adaptivity is presented, based on the summation-by-parts-simultaneous approximation term (SBP-SAT) methodology. The accuracy and the robustness of the numerical method are investigated.
eSSENCE
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FERRERO, ANDREA. "Computational fluid dynamics for aerospace propulsion systems: an approach based on discontinuous finite elements." Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2598559.

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The purpose of this work is the development of a numerical tool devoted to the study of the flow field in the components of aerospace propulsion systems. The goal is to obtain a code which can efficiently deal with both steady and unsteady problems, even in the presence of complex geometries. Several physical models have been implemented and tested, starting from Euler equations up to a three equations RANS model. Numerical results have been compared with experimental data for several real life applications in order to understand the range of applicability of the code. Performance optimization has been considered with particular care thanks to the participation to two international Workshops in which the results were compared with other groups from all over the world. As far as the numerical aspect is concerned, state-of-art algorithms have been implemented in order to make the tool competitive with respect to existing softwares. The features of the chosen discretization have been exploited to develop adaptive algorithms (p, h and hp adaptivity) which can automatically refine the discretization. Furthermore, two new algorithms have been developed during the research activity. In particular, a new technique (Feedback filtering [1]) for shock capturing in the framework of Discontinuous Galerkin methods has been introduced. It is based on an adaptive filter and can be efficiently used with explicit time integration schemes. Furthermore, a new method (Enhance Stability Recovery [2]) for the computation of diffusive fluxes in Discontinuous Galerkin discretizations has been developed. It derives from the original recovery approach proposed by van Leer and Nomura [3] in 2005 but it uses a different recovery basis and a different approach for the imposition of Dirichlet boundary conditions. The performed numerical comparisons showed that the ESR method has a larger stability limit in explicit time integration with respect to other existing methods (BR2 [4] and original recovery [3]). In conclusion, several well known test cases were studied in order to evaluate the behavior of the implemented physical models and the performance of the developed numerical schemes.
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Ojeda, Steven Matthew. "A cut-cell method for adaptive high-order discretizations of conjugate heat transfer problems." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90783.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 143-151).
Heat transfer between a conductive solid and an adjacent convective fluid is prevalent in many aerospace systems. The ability to achieve accurate predictions of the coupled heat interaction is critical in advancing thermodynamic designs. Despite their growing use, coupled fluid-solid analyses known as conjugate heat transfer (CHT) are hindered by the lack of automation and robustness. The mesh generation process is still highly dependent on user experience and resources, requiring time-consuming involvement in the analysis cycle. This thesis presents work toward developing a robust PDE solution framework for CHT simulations that autonomously provides reliable output predictions. More specifically, the framework is comprised of the following components: a simplex cut-cell technique that generates multi-regioned meshes decoupled from the design geometry, a high-order discontinuous Galerkin (DG) discretization, and an anisotropic output-based adaptation method that autonomously adapts the mesh to minimize the error in an output of interest. An existing cut-cell technique is first extended to generate fully-embedded meshes with multiple sub-domains. Then, a coupled framework that combines separate disciplines is developed, while ensuring compatibility between the cut-cell and mesh adaptation algorithms. Next, the framework is applied to high-order discretizations of the heat, Navier-Stokes, and Reynolds-Averaged Navier-Stokes (RANS) equations to analyze the heat flux interaction. Through a series of numerical studies, high-order accurate outputs solved on autonomously controlled cut-cell meshes are demonstrated. Finally, the conjugate solutions are analyzed to gain physical insight to the coupled interaction.
by Steven Matthew Ojeda.
S.M.
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Fidkowski, Krzysztof J. 1981. "A simplex cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/39701.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.
Includes bibliographical references (p. 169-175).
While an indispensable tool in analysis and design applications, Computational Fluid Dynamics (CFD) is still plagued by insufficient automation and robustness in the geometry-to-solution process. This thesis presents two ideas for improving automation and robustness in CFD: output-based mesh adaptation for high-order discretizations and simplex, cut-cell mesh generation. First, output-based mesh adaptation consists of generating a sequence of meshes in an automated fashion with the goal of minimizing an estimate of the error in an engineering output. This technique is proposed as an alternative to current CFD practices in which error estimation and mesh generation are largely performed by experienced practitioners. Second, cut-cell mesh generation is a potentially more automated and robust technique compared to boundary-conforming mesh generation for complex, curved geometries. Cut-cell meshes are obtained by cutting a given geometry of interest out of a background mesh that need not conform to the geometry boundary. Specifically, this thesis develops the idea of simplex cut cells, in which the background mesh consists of triangles or tetrahedra that can be stretched in arbitrary directions to efficiently resolve boundary-layer and wake features.
(cont.) The compressible Navier-Stokes equations in both two and three dimensions are discretized using the discontinuous Galerkin (DG) finite element method. An anisotropic h-adaptation technique is presented for high-order (p > 1) discretizations, driven by an output-error estimate obtained from the solution of an adjoint problem. In two and three dimensions, algorithms are presented for intersecting the geometry with the background mesh and for constructing the resulting cut cells. In addition, a quadrature technique is proposed for accurately integrating high-order functions on arbitrarily-shaped cut cells and cut faces. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard, boundary-conforming meshes. In two dimensions, robustness of the cut-cell, adaptive technique is successfully tested for highly-anisotropic boundary-layer meshes representative of practical high-Re simulations. In three dimensions, robustness of cut cells is demonstrated for various representative curved geometries. Adaptation results show that for all test cases considered, p = 2 and p = 3 discretizations meet desired error tolerances using fewer degrees of freedom than p = 1.
Krzysztof Jakub Fidkowski.
Ph.D.
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Sun, Huafei. "A robust simplex cut-cell method for adaptive high-order discretizations of aerodynamics and multi-physics problems." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/85764.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 189-199).
Despite the wide use of partial differential equation (PDE) solvers, lack of automation still hinders realizing their full potential in assisting engineering analysis and design. In particular, the process of establishing a suitable mesh for a given problem often requires heavy person-in-the-loop involvement. This thesis presents work toward the development of a robust PDE solution framework that provides a reliable output prediction in a fully-automated manner. The framework consists of: a simplex cut-cell technique which allows the mesh generation process to be independent of the geometry of interest; a discontinuous Galerkin (DG) discretization which permits an easy extension to high-order accuracy; and an anisotropic output-based adaptation which improves the discretization mesh for an accurate output prediction in a fully-automated manner. Two issues are addressed that limit the automation and robustness of the existing simplex cut-cell technique in three dimensions. The first is the intersection ambiguity due to numerical precision. We introduce adaptive precision arithmetic that guarantees intersection correctness, and develop various techniques to improve the efficiency of using this arithmetic. The second is the poor quadrature quality for arbitrarily shaped elements. We propose a high-quality and efficient cut-cell quadrature rule that satisfies a quality measure we define, and demonstrate the improvement in nonlinear solver robustness using this quadrature rule. The robustness and automation of the solution framework is then demonstrated through a range of aerodynamics problems, including inviscid and laminar flows. We develop a high-order DG method with a dual-consistent output evaluation for elliptic interface problems, and extend the simplex cut-cell technique for these problems, together with a metric-optimization adaptation algorithm to handle cut elements. This solution strategy is further extended for multi-physics problems, governed by different PDEs across the interfaces. Through numerical examples, including elliptic interface problems and a conjugate heat transfer problem, high-order accuracy is demonstrated on non-interface-conforming meshes constructed by the cut-cell technique, and mesh element size and shape on each material are automatically adjusted for an accurate output prediction.
by Huafei Sun.
Ph. D.
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Li, Jizhou. "Locally Mass-Conservative Method With Discontinuous Galerkin In Time For Solving Miscible Displacement Equations Under Low Regularity." Thesis, 2013. http://hdl.handle.net/1911/71985.

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The miscible displacement equations provide the mathematical model for simulating the displacement of a mixture of oil and miscible fluid in underground reservoirs during the Enhance Oil Recovery(EOR) process. In this thesis, I propose a stable numerical scheme combining a mixed finite element method and space-time discontinuous Galerkin method for solving miscible displacement equations under low regularity assumption. Convergence of the discrete solution is investigated using a compactness theorem for functions that are discontinuous in space and time. Numerical experiments illustrate that the rate of convergence is improved by using a high order time stepping method. For petroleum engineers, it is essential to compute finely detailed fluid profiles in order to design efficient recovery procedure thereby increase production in the EOR process. The method I propose takes advantage of both high order time approximation and discontinuous Galerkin method in space and is capable of providing accurate numerical solutions to assist in increasing the production rate of the miscible displacement oil recovery process.
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Books on the topic "High-order discretization methods"

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Strong stability preserving high-order time discretization methods. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2000.

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Tam, Anita W. High-order spatial discretization methods for the shallow water equations. 2001.

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Book chapters on the topic "High-order discretization methods"

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Sjögreen, Björn, and H. C. Yee. "High Order Compact Central Spatial Discretization Under the Framework of Entropy Split Methods." In Lecture Notes in Computational Science and Engineering, 439–54. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-20432-6_29.

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Deville, Michel O. "Instability." In An Introduction to the Mechanics of Incompressible Fluids, 197–210. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04683-4_8.

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AbstractThe first instability mechanism is applied to the plane parallel channel flow. We establish the well known Orr-Sommerfeld equation which is solved by the Chebyshev Tau method. The associated Fortran programme is given in the appendix. Then the stability of the circular Couette flow between two concentric cylinders is undertaken. The inviscid approach yields the Rayleigh stability criterion. The incorporation of the viscous and pressure terms generates through a linearization process a set of differential equations again solved by high-order discretization methods through a generalized eigenvalue problem. The chapter ends with the case of the non-linear axisymmetric Taylor vortices.
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Löhner, Rainald. "High-Order Methods for Simulations in Engineering." In Efficient High-Order Discretizations for Computational Fluid Dynamics, 277–307. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60610-7_7.

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Seitz, Timo, Ansgar Lechtenberg, and Peter Gerlinger. "Rocket Combustion Chamber Simulations Using High-Order Methods." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 381–94. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53847-7_24.

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Abstract High-order spatial discretizations significantly improve the accuracy of flow simulations. In this work, a multi-dimensional limiting process with low diffusion (MLP$$^\text {ld}$$) and up to fifth order accuracy is employed. The advantage of MLP is that all surrounding volumes of a specific volume may be used to obtain cell interface values. This prevents oscillations at oblique discontinuities and improves convergence. This numerical scheme is utilized to investigate three different rocket combustors, namely a seven injector methane/oxygen combustion chamber, the widely simulated PennState preburner combustor and a single injector chamber called BKC, where pressure oscillations are important.
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Kronbichler, Martin. "The Discontinuous Galerkin Method: Derivation and Properties." In Efficient High-Order Discretizations for Computational Fluid Dynamics, 1–55. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60610-7_1.

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Fernández-Méndez, Sonia. "An Introduction to the Hybridizable Discontinuous Galerkin Method." In Efficient High-Order Discretizations for Computational Fluid Dynamics, 261–75. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60610-7_6.

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Kronbichler, Martin. "High-Performance Implementation of Discontinuous Galerkin Methods with Application in Fluid Flow." In Efficient High-Order Discretizations for Computational Fluid Dynamics, 57–115. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60610-7_2.

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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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Su, Penghui, and Liang Zhang. "A Discontinuous Galerkin Method on Arbitrary Grids with High Order Boundary Discretization." In Lecture Notes in Electrical Engineering, 591–600. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3305-7_48.

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Ksiezyk, Mariusz, and Artur Tyliszczak. "LES of a Converging–Diverging Channel Performed with the Immersed Boundary Method and a High-Order Compact Discretization." In Progress in Wall Turbulence 2, 191–200. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20388-1_17.

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Conference papers on the topic "High-order discretization methods"

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May, G., F. Iacono, A. Balan, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Time-Relaxation Methods for High-Order Discretization of Compressible Flow Problems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636881.

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Costa Nogueira Junior, Alberto, Jonathan Bernardo, and Stephen Moore. "Modelling Traffic Flow with the Nonlinear LWR Scheme using the High Order Discontinuous Galerkin Discretization." In XXXVI Iberian Latin American Congress on Computational Methods in Engineering. Rio de Janeiro, Brazil: ABMEC Brazilian Association of Computational Methods in Engineering, 2015. http://dx.doi.org/10.20906/cps/cilamce2015-0232.

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Marty, Julien, Nicolas Lantos, Bertrand Michel, and Virginie Bonneau. "LES and Hybrid RANS/LES Simulations of Turbomachinery Flows Using High Order Methods." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42134.

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The flow within turbomachinery applications is intrinsically complex and unsteady, and involves boundary layer transition, separation and vortices such as tip leakage vortex and wakes. Recent investigations show that Large Eddy Simulation and hybrid RANS/LES methods are required to accurately capture such flows. It is well-known that the numerical dissipation coming from the spatial discretization scheme must not be excessive because it can have a significant influence on the results. The present investigation assesses the impact of upwind spatial discretization scheme AUSM+(P) with high-order MUSCL extension at third- and fifth-order applied to different turbomachinery cases: (i) Large Eddy Simulation (LES) of laminar separation bubble over the high-lift low-pressure turbine airfoil T106C. The present investigation shows that the MUSCL extension to high-order is compatible with no-match boundaries and solution accuracy is not impacted. (ii) Zonal Detached Eddy Simulation (ZDES) of the first rotor of the transonic research compressor CREATE. Since a shock is present near the blade tip, a mixed scheme is developed in order to improve the robustness of the high-order scheme. The spectral analysis shows that the high-order scheme improves the resolution of small vortical structures. (iii) Zonal Detached Eddy Simulation of a fan rotor in order to well predict the broadband noise due the interaction between the fan wake and the OGV. Third and fifth order schemes are compared for both aerodynamic and acoustic purposes. The wake is well captured by the ZDES method and the velocity power spectral density is well predicted with this advanced method.
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Kollmannsberger, Stefan, Alexander Du¨ster, and Ernst Rank. "Force Transfer for High Order Finite Element Methods Using Intersected Meshes." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26539.

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High order Finite Element Methods have been shown to be an efficient approach for computing the behavior of fluids and structures alike. However the coupling of such methods in a framework for a partitioned fluid-structure interaction is still in its early stages. A difficulty hereby is a conservative transfer of the loads from the fluid to the solid and an appropriate transfer of the structural displacements back to the boundary of the fluid. This contribution describes the coupling of a high order finite element structural code to the commercial finite volume fluid solver CFX and focuses on the transfer of the loads. For this purpose, the fluid mesh and the structural mesh are intersected. The force acting on the solid is then computed by a composed integration scheme performed on the intersected mesh. The approach can be interpreted as a projection method taking into account the discretization on both sides, i.e. fluid and solid. Numerical examples will demonstrate the basic properties of this new type of data transfer.
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Ijaz, Muhammad, and N. K. Anand. "Simulation of Unsteady Incompressible Viscous Flow Using Higher Order Implicit Runge-Kutta Methods: Staggered Grid." In ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference collocated with the ASME 2007 InterPACK Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ht2007-32486.

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A numerical method (SIMPLE DIRK Method) for transient incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently available simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme of Patankar [2] was used for spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial CFD software, FLUENT [3] using second-order implicit time discretization scheme. Steady state solution from the present method was compared with the benchmark numerical solution of Ghia et al. [4]. Good agreement of the second-order solutions of the proposed method with the second-order solutions of FLUENT [4] and Ghia et al. [4] concludes the feasibility of the proposed method.
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Bagheri-Sadeghi, Nojan, Brian T. Helenbrook, and Kenneth D. Visser. "Turbulent Channel Flow With a Modified k-ω Turbulence Model for High-Order Finite Element Methods." In ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/ajkfluids2019-5501.

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Abstract One-dimensional fully developed channel flow was solved using a modified k–ω turbulence model that was recently proposed for use with high-order finite element schemes. In order to study this new turbulence model’s behavior, determine its dependence on boundary conditions and model constants, and find efficient methods for obtaining solutions, the model was first examined using a linear finite element discretization in 1D. The results showed that an accurate estimate of the parameter εk which is used to define k in terms of the working variable k~ is essential to get an accurate solution. Also, the turbulence model depended sensitively on an accurate estimate of the distance of the first grid point from the wall, which can be difficult to estimate in unstructured grids. This is used for the boundary condition of specific dissipation rate on the wall. This model was then implemented in a high-order finite element code that uses an unstructured mesh of triangles to verify that the 1D results were predictive of the behavior of the full 2D discretization. High-order 2D results were obtained on triangular meshes with element aspect ratios up to 250000.
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Byun, Jaeseung, and Carlos Pantano. "Advanced and high-order numerical discretization methods for large-eddy simulation that maximize subgrid-scale model resolution." In 21st AIAA Computational Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-2725.

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Wang, Baokun, Shaohua Wang, and Ying Luo. "Design and High Accuracy Numerical Implementation of Fractional Order PI Controller for a PMSM Speed System." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-71115.

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Abstract In this paper, a systematic design and high accuracy implementation of fractional order proportional integral (FOPI) controller is proposed for a permanent magnet synchronous motor (PMSM) speed system, and the numerical implementation performance of the fractional order operator is evaluated with comprehensive investigation using different implementation methods. Three commonly used numerical implementation methods of fractional operators are investigated and compared in this paper. Futhermore, for the impulse response invariant method, the effects of different discretization orders on the system control performance are compared. The simulation results show that the high accuracy numerical implementation method of the designed high-order FOPI controller has improved performance over normal accuracy fractional order operation implementation.
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Costa Nogueira Junior, Alberto, João Lucas De Sousa Almeida, and Cláudio Alessandro De Carvalho Silva. "ON THE CHOICE OF SHOCK CAPTURING SCHEMES FOR THE SOLUTION OF THE LWR TRAFFIC FLOW EQUATION USING A HIGH ORDER MODAL DISCONTINUOUS GALERKIN DISCRETIZATION." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2392.8319.

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Yang, H. Q., Z. J. Chen, and Jonathan G. Dudley. "Development of High-Order Scheme in Unstructured Mesh for Direct Numerical Simulations." In ASME 2013 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fedsm2013-16386.

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There has been a growing interest in higher-order spatial discretization methods due to their potential for delivering high accuracy at reasonable computational overhead for the Direct Numerical Simulation (DNS) of vortex-dominated flows. Many of the existing high-order schemes for unstructured grids use more degrees-of-freedom (DOF) in each cell to achieve high-order accuracy. This paper formulates and demonstrates a high-order correction method for unstructured grids. Using this approach, there is no increase in DOF within each cell. By adding higher order correction terms, higher order accuracy can be achieved. The present technique is innovative in that it can be readily added to existing lower order solvers, it can achieve very high-order accuracy, it is stable, and it can make use of either central or upwind schemes. Many examples are presented and used to demonstrate the high-order accuracy.
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Reports on the topic "High-order discretization methods"

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May, Georg. High Order Methods for Compressible Viscous Flow on Unstructured Meshes: New Discretization Techniques and Algorithms. Fort Belvoir, VA: Defense Technical Information Center, February 2014. http://dx.doi.org/10.21236/ada607457.

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Соловйов, Володимир Миколайович, Vladimir Saptsin, and Dmitry Chabanenko. Prediction of financial time series with the technology of high-order Markov chains. AGSOE, March 2009. http://dx.doi.org/10.31812/0564/1131.

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In this research the technology of complex Markov chains, i.e. Markov chains with a memory is applied to forecast the financial time-series. The high-order Markov chains can be simplified to first-order ones by generalizing the states in Markov chains. Considering the *generalized state* as the sequence of states makes a possibility to model high-order Markov chains like first-order ones. The adaptive method of defining the states is proposed, it is concerned with the statistic properties of price returns. The algorithm of prediction includes the next steps: (1) Generate the hierarchical set of time discretizations; (2) Reducing the discretiza- tion of initial data and doing prediction at the every time-level (3) Recurrent conjunction of prediction series of different discretizations in a single time-series. The hierarchy of time discretizations gives a possibility to review long-memory properties of the series without increasing the order of the Markov chains, to make prediction on the different frequencies of the series. The technology is tested on several time-series, including: EUR/USD Forex course, the World’s indices, including Dow Jones, S&P 500, RTS, PFTS and other.
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Ray, Jaideep, Sophia Lefantzi, Habib N. Najm, and Christopher A. Kennedy. Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters. Office of Scientific and Technical Information (OSTI), January 2006. http://dx.doi.org/10.2172/877727.

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