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.
Find full textVanharen, 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.
Full textHao, Zhaopeng. "High-order numerical methods for integral fractional Laplacian: algorithm and analysis." Digital WPI, 2020. https://digitalcommons.wpi.edu/etd-dissertations/612.
Full textJunior, 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.
Full textLundquist, 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.
Full textVadsola, 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.
Full textHarris, Robert Evan. "An adaptive quadrature-free implementation of the high-order spectral volume method on unstructured grids." [Ames, Iowa : Iowa State University], 2008.
Find full textThomas, 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.
Full textThomas, 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.
Full textBarnes, 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.
Full textHuismann, Immo. "Computational fluid dynamics on wildly heterogeneous systems." TUDPress, 2018. https://tud.qucosa.de/id/qucosa%3A74002.
Full textSingh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.
Full textVazquez, Thais Godoy. "Funções de interpolação e regras de integração tensorizaveis para o metodo de elementos finitos de alta ordem." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263500.
Full textTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
Made available in DSpace on 2018-08-10T12:57:32Z (GMT). No. of bitstreams: 1 Vazquez_ThaisGodoy_D.pdf: 11719751 bytes, checksum: c6d385d6a6414705c9f468358b8d3bea (MD5) Previous issue date: 2008
Resumo: Este trabalho tem por objetivo principal o desenvolvimento de funções de interpolaçao e regras de integraçao tensorizaveis para o Metodo dos Elementos Finitos (MEF) de alta ordem hp, considerando os sistemas de referencias locais dos elementos. Para isso, primeiramente, determinam-se ponderaçoes especficas para as bases de funçoes de triangulos e tetraedros, formada pelo produto tensorial de polinomios de Jacobi, de forma a se obter melhor esparsidade e condicionamento das matrizes de massa e rigidez dos elementos. Alem disso, procuram-se novas funçoes de base para tornar as matrizes de massa e rigidez mais esparsas possiveis. Em seguida, escolhe-se os pontos de integraçao que otimizam o custo do calculo dos coeficientes das matrizes de massa e rigidez usando as regras de quadratura de Gauss-Jacobi, Gauss-Radau-Jacobi e Gauss-Lobatto-Jacobi. Por fim, mostra-se a construçao de uma base unidimensional nodal que permite obter uma matriz de rigidez praticamente diagonal para problemas de Poisson unidimensionais. Discute-se ainda extensoes para elementos bi e tridimensionais
Abstract: The main purpose of this work is the development of tensor-based interpolation functions and integration rules for the hp High-order Finite Element Method (FEM), considering the local reference systems of the elements. We first determine specific weights for the shape functions of triangles and tetrahedra, constructed by the tensorial product of Jacobi polynomials, aiming to obtain better sparsity and numerical conditioning for the mass and stiffness matrices of the elements. Moreover, new shape functions are proposed to obtain more sparse mass and stiffness matrices. After that, integration points are chosen that optimize the cost for the calculation of the coefficients of the mass and stiffness matrices using the rules of quadrature of Gauss-Jacobi, Gauss-Radau-Jacobi and Gauss-Lobatto-Jacobi. Finally, we construct an one-dimensional nodal shape function that obtains an almost diagonal stiffness matrix for the 1D Poisson problem. Extensions to two and three-dimensional elements are discussed.
Doutorado
Mecanica dos Sólidos e Projeto Mecanico
Doutor em Engenharia Mecânica
Bassili, Niclas, and Douglas Eriksson. "An evaluation of deterministic prediction of ocean waves using pressure data to assist a Wave Energy Converter." Thesis, KTH, Skolan för industriell teknik och management (ITM), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-279600.
Full textNuvarande enheter för att extrahera elektrisk energi från havsvågor lider av stora problem med låg effektivitet på grund av brist på information om de inkommande vågorna. Det komplexa ickelinjära dynamiska beteendet hos havsvågor gör förutsägelsen av dem till en stor utmaning. Det här arbetet syftar till att undersöka ett deterministiskt kortsiktigt system för att förutspå våg för våg, som noggrant kan förutspå våghöjd och tidpunkt för de inkommande vågorna, baserat på mätdata från en dränkbar trycksensor. Den kompletta förutsägelseprocessen innehåller tre steg, rekonstruktion, assimilering och förutsägelse. En ickelinjär weakly dispersive reconstruction method används först för att med hög noggrannhet beräkna ythöjningen från det uppmätta trycket. Därefter, används en variational assimilation method för att konvertera en tidsserie av ythöjningen till ett rumsligt vågfält, för att erhålla initialvillkor för förutsägelsen. Slutligen används en High Order Spectral Method för att deterministiskt förutspå utvecklingen av det tvådimensionella oregelbundna vågfältet baserat på de förvärvade initialvillkoren. För att verifiera prestandan av det föreslagna förutsägelsesystemet, så genomfördes tester med data från olika oregelbundna havstillstånd med varierande parametrar, genererade av simuleringar, såväl som modellexperiment utförda i en kontrollerad miljö i form av en vågtank. Resultaten från testerna visar att ythöjningen förutspås inom 5% från referensen, för en period på 10 sekunder framåt i tiden, för vågor som ett vågkraftverk vanligtvis utsätts för. Baserat på resultatet, så är det möjligt att förutspå inkommande vågor, men noggrannheten beror kraftigt på det aktuella havstillståndet och det valda avståndet för förutsägelsen. Resultaten har jämförts mot liknande tester gjorda med radardata och visat sig vara ett genomförbart alternativ för vissa havstillstånd. Sammanfattningsvis visas det att tryckmätningar, som ett medel för att mäta ett havsvågfält, är ett bra alternativ när de kombineras med ickelinjära rekonstruktions- och förutsägelsemetoder för att hjälpa till att öka ett vågkraftverks energigenerering.
Akeab, Imad. "High frequency scattering and spectral methods." Doctoral thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-57871.
Full textPostell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.
Full textRossi, Lorenzo. "Functional renormalization group: higher order flows and pseudo-spectral methods." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18120/.
Full textStrauss, Michael. "Spectral pollution and higher order projection methods for operator pencils." Thesis, King's College London (University of London), 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497989.
Full textKudo, Jun S. M. Massachusetts Institute of Technology. "Robust adaptive high-order RANS methods." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/95563.
Full textCataloged from PDF version of thesis.
Includes bibliographical references (pages 89-94).
The ability to achieve accurate predictions of turbulent flow over arbitrarily complex geometries proves critical in the advancement of aerospace design. However, quantitatively accurate results from modern Computational Fluid Dynamics (CFD) tools are often accompanied by intractably high computational expenses and are significantly hindered by the lack of automation. In particular, the generation of a suitable mesh for a given flow problem often requires significant amounts of human input. This process however encounters difficulties for turbulent flows which exhibit a wide range of length scales that must be spatially resolved for an accurate solution. Higher-order adaptive methods are attractive candidates for addressing these deficiencies by promising accurate solutions at a reduced cost in a highly automated fashion. However, these methods in general are still not robust enough for industrial applications and significant advances must be made before the true realization of robust automated three-dimensional turbulent CFD. This thesis presents steps towards this realization of a robust high-order adaptive Reynolds-Averaged Navier-Stokes (RANS) method for the analysis of turbulent flows. Specifically, a discontinuous Galerkin (DG) discretization of the RANS equations and an output-based error estimation with an associated mesh adaptation algorithm is demonstrated. To improve the robustness associated with the RANS discretization, modifications to the negative continuation of the Spalart-Allmaras turbulence model are reviewed and numerically demonstrated on a test case. An existing metric-based adaptation framework is adopted and modified to improve the procedure's global convergence behavior. The resulting discretization and modified adaptation procedure is then applied to two-dimensional and three-dimensional turbulent flows to demonstrate the overall capability of the method.
by Jun Kudo.
S.M.
Bissessur, Prithiraj. "Unsteady aerodynamics using high-order methods." Thesis, University of Southampton, 2007. https://eprints.soton.ac.uk/49924/.
Full textVillardi, de Montlaur Adeline de. "High-order discontinuous Galerkin methods for incompressible flows." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5928.
Full textEs desenvolupa un nou mètode de DG amb penalti interior (IPM-DG), que condueix a una forma feble simètrica i coerciva pel terme de difusió, i que permet assolir una aproximació espacial d'alt ordre. Aquest mètode s'aplica per resoldre les equacions de Stokes i Navier-Stokes. L'espai d'aproximació de la velocitat es descompon dins de cada element en una part solenoidal i una altra irrotacional, de manera que es pot dividir la forma dèbil IPM-DG en dos problemes desacoblats. El primer permet el càlcul de les velocitats i de les pressions híbrides, mentre que el segon calcula les pressions en l'interior dels elements. Aquest desacoblament permet una reducció important del número de graus de llibertat tant per velocitat com per pressió. S'introdueix també un paràmetre extra de penalti resultant en una formulació DG alternativa per calcular les velocitats solenoidales, on les pressions no apareixen. Les pressions es poden calcular com un post-procés de la solució de les velocitats. Es contemplen altres formulacions DG, com per exemple el mètode Compact Discontinuous Galerkin, i es comparen al mètode IPM-DG.
Es proposen mètodes implícits de Runge-Kutta d'alt ordre per problemes transitoris incompressibles, permetent obtenir esquemes incondicionalment estables i amb alt ordre de precisió temporal. Les equacions de Navier-Stokes incompressibles transitòries s'interpreten com un sistema de Equacions Algebraiques Diferencials, és a dir, un sistema d'equacions diferencials ordinàries corresponent a la equació de conservació del moment, més les restriccions algebraiques corresponent a la condició d'incompressibilitat.
Mitjançant exemples numèrics es mostra l'aplicabilitat de les metodologies proposades i es comparen la seva eficiència i precisió.
This PhD thesis proposes divergence-free Discontinuous Galerkin formulations providing high orders of accuracy for incompressible viscous flows.
A new Interior Penalty Discontinuous Galerkin (IPM-DG) formulation is developed, leading to a symmetric and coercive bilinear weak form for the diffusion term, and achieving high-order spatial approximations. It is applied to the solution of the Stokes and Navier-Stokes equations. The velocity approximation space is decomposed in every element into a solenoidal part and an irrotational part. This allows to split the IPM weak form in two uncoupled problems. The first one solves for velocity and hybrid pressure, and the second one allows the evaluation of pressures in the interior of the elements. This results in an important reduction of the total number of degrees of freedom for both velocity and pressure.
The introduction of an extra penalty parameter leads to an alternative DG formulation for the computation of solenoidal velocities with no presence of pressure terms. Pressure can then be computed as a post-process of the velocity solution. Other DG formulations, such as the Compact Discontinuous Galerkin method, are contemplated and compared to IPM-DG.
High-order Implicit Runge-Kutta methods are then proposed to solve transient incompressible problems, allowing to obtain unconditionally stable schemes with high orders of accuracy in time. For this purpose, the unsteady incompressible Navier-Stokes equations are interpreted as a system of Differential Algebraic Equations, that is, a system of ordinary differential equations corresponding to the conservation of momentum equation, plus algebraic constraints corresponding to the incompressibility condition.
Numerical examples demonstrate the applicability of the proposed methodologies and compare their efficiency and accuracy.
Svärd, Magnus. "Stable High-Order Finite Difference Methods for Aerodynamics." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4621.
Full textSvärd, Magnus. "Stable high-order finite difference methods for aerodynamics /." Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4621.
Full textMatar, Samir A. "Numerical methods for high-order boundary-value problems." Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293058.
Full textIqbal, Kashif H. "Comparison of high-order methods on unstructured grids." Thesis, Cranfield University, 2013. http://dspace.lib.cranfield.ac.uk/handle/1826/8274.
Full textVelechovsky, Jan. "High-order numerical methods for laser plasma modeling." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0098/document.
Full textThis thesis presents the overview and the original contributions to a high–orderArbitrary Lagrangian–Eulerian (ALE) method applicable for the laser–generated plasma modeling withthe focus to a remapping step of the ALE method. The remap is the conservative interpolation of theconservative quantities from a low–quality Lagrangian grid onto a better, smoothed one. To avoidnon–physical numerical oscillations, the high–order numerical fluxes of the reconstruction arecombined with the low–order (first–order) numerical fluxes produced by a standard donor remappingmethod. The proposed method for a cell–centered discretization preserves bounds for the density,velocity and specific internal energy by its construction. Particular symmetry–preserving aspects of themethod are applied for a staggered momentum remap. The application part of the thesis is devoted tothe laser radiation absorption modeling in plasmas and microstructures materials with the particularinterest in the laser absorption in low–density foams. The absorption is modeled on two spatial scalessimultaneously. This two–scale laser absorption model is implemented in the hydrodynamic codePALE. The numerical simulations of the velocity of laser penetration in a low–density foam are in agood agreement with the experimental data
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.
Full textTsoutsanis, Panagiotis. "Very high-order methods for 3D arbitrary unstructured grids." Thesis, Cranfield University, 2009. http://hdl.handle.net/1826/4511.
Full textBowen, Matthew K. "High-order finite difference methods for partial differential equations." Thesis, Loughborough University, 2005. https://dspace.lboro.ac.uk/2134/13492.
Full textMazzieri, Ilario. "Non-conforming high order methods for the elastodynamics equation." Nice, 2012. http://www.theses.fr/2012NICE4014.
Full textIn this thesis, we present a new discretization approach to combine the Discontinuous Galerkin Spectral Element (DGSE) and the Mortar Spectral Element (MSE) methods with suitable time advancing schemes for the simulation of the elastic wave propagation in heterogeneous media. To overcome the limitations of the existing approaches we apply the non-conforming paradigm only at the subdomain level. We show that the resulting formulations are stable, enjoy optimal approximation properties, and suffer from low dispersion and dissipation errors. Applications of the DGSE and MSE methods to simulate realistic seismic wave propagation problems in three dimensions are also considered
Grundvig, Dane Scott. "High Order Numerical Methods for Problems in Wave Scattering." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8617.
Full textRiera, Pau. "Conservative high order collocation methods for nonlinear Schrödinger equations." Thesis, Stockholms universitet, Fysikum, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-194703.
Full textVila, Pérez Jordi. "Low and high-order hybridised methods for compressible flows." Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/671889.
Full textLa comunitat aeroespacial té el repte a dia d’avui de poder tractar amb precisió simulacions de mecànica de fluids computacional (CFD) de problemes de flux compressible en càlcul nocturn. Programes convencionals de simulació CFD basats en mètodes de volums finits (VF) de segon ordre ofereixen aproximacions precises de fluxos turbulents estacionaris però són incapaços de produir prediccions fidels de l’entorn de vol complet. Alternativament, les discretitzations prometedores d’alt ordre, de les quals s’espera que permetin simulacions accessibles d’alta fidelitat per a fluxos turbulents transitoris, encara estan subjectes a fortes limitacions en eficiència i robustesa, delimitant-ne el nivell de maduresa encara lluny de requeriments industrials. En conseqüència, el paradigma del CFD es troba immers ara mateix en la cruïlla delimitada per les limitacions inherents dels mètodes de baix ordre i l’estat encara immadur de les discretitzacions d’alt ordre. D’acord amb això, aquesta tesi desenvolupa una estratègia doble per a la simulació d’alta fidelitat de flux compressible introduint dues metodologies, als nivells de baix i alt ordre, respectivament, basades en formulacions híbrides. Primer, es proposa un nou paradigma de VF, el mètode de volums finits centrats en les cares (FCFV), per a la formulació de fluxos compressible estacionaris. Aquesta metodologia descriu una formulació mixta híbrida de VF que, seguint un procés d’hibridització, defineix les incògnites del problema als baricentres de les cares. Les variables del problema -quantitats conservatives i tensor de tensions i flux de calor en el cas viscós- són obtingudes amb precisió òptima de primer ordre dins de cada element mitjançant una etapa de postprocessat de cost reduït sense la necessitat de reconstrucció dels gradients. Amb això, el mètode FCFV preserva la qualitat de l’aproximació fins i tot en presència d’elements amb un alt estretament o distorsió, donant lloc a un mètode insensible a la qualitat de la malla. A més a més, el mètode de FCFV és un esquema preservador de monotonia, donant lloc a aproximacions no oscil·latòries de forts gradients sense necessitat d’utilitzar mètodes de captura de xocs o limitadors. Finalment, el mètode és robust en el límit incompressible i és capaç de calcular amb precisió solucions de fluxos amb nombre de Mach baix sense haver d’introduir estratègies específiques de correcció de pressió. En paral·lel, es presenta una revisió del mètode híbrid de Galerkin discontinu (HDG) d’alt ordre en el context de flux compressible, presentant un marc unificat per a la derivació de fluxos numèrics del problema de Riemann en formulacions híbrides. El marc inclou per primera vegada en un entorn HDG, els fluxos numèrics d’HLL i HLLEM, així com els tradicionals de Lax-Friedrichs i Roe. Es mostren les propietats de preservació de positivitat dels fluxos de tipus HLL, que demostren la seva superioritat respecte els de Roe en casos supersònics. Addicionalment, el mètode d’HLLEM destaca especialment en l’aproximació de capes límit com a resultat de la seva preservació d’esforços tallants, la qual li confereix una precisió afegida respecte les d’HLL i Lax-Friedrichs. Al llarg de l’estudi s’introdueix una llista extensa d’exemples numèrics de referència d’interès pràctic per tal de validar les propostes en baix i alt ordre. Es presenten diferents exemples de flux compressible en una gran varietat de règims, des de flux invíscid fins a flux laminar viscós, des de velocitats subsòniques fins a supersòniques, per tal de verificar la precisió de les metodologies proposades i el rendiment dels fluxos numèrics introduïts
Hyde, Edward McKay Bruno Oscar P. "Fast, high-order methods for scattering by inhomogeneous media /." Diss., Pasadena, Calif. : California Institute of Technology, 2003. http://resolver.caltech.edu/CaltechETD:etd-08142002-182101.
Full textLin, Yuan. "High-order finite difference methods for solving heat equations /." Available to subscribers only, 2008. http://proquest.umi.com/pqdweb?did=1559848541&sid=1&Fmt=2&clientId=1509&RQT=309&VName=PQD.
Full text"Department of Mathematics." Keywords: High-order finite difference, Heat equations Includes bibliographical references (p. 64-68). Also available online.
Zachariadis, Zacharias Ioannis. "High resolution and high order methods for RANS modelling and aerodynamic optimization." Thesis, Cranfield University, 2008. http://hdl.handle.net/1826/3806.
Full textWang, Tengyao. "Spectral methods and computational trade-offs in high-dimensional statistical inference." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/260825.
Full textChiang, Weng Cheng Venus. "High-order finite difference methods for solving convection diffusion equations." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1807119.
Full textWeggler, Lucy Verfasser], and Sergej [Akademischer Betreuer] [Rjasanow. "High order boundary element methods / Lucy Weggler. Betreuer: Sergej Rjasanow." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2012. http://d-nb.info/1051586801/34.
Full textRothauge, Kai. "The discrete adjoint method for high-order time-stepping methods." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/60285.
Full textScience, Faculty of
Mathematics, Department of
Graduate
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.
Full textMattsson, Ken. "Summation-by-Parts Operators for High Order Finite Difference Methods." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3434.
Full textMarais, Neilen. "Efficient high-order time domain finite element methods in electromagnetics." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/1499.
Full textThe Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can beused to solve a large class of Electromagnetics problems with high accuracy and good computational efficiency. For solving wide-band problems time domain solutions are often preferred; while time domain FEM methods are feasible, the Finite Difference Time Domain (FDTD) method is more commonly applied. The FDTD is popular both for its efficiency and its simplicity. The efficiency of the FDTD stems from the fact that it is both explicit (i.e. no matrices need to be solved) and second order accurate in both time and space. The FDTD has limitations when dealing with certain geometrical shapes and when electrically large structures are analysed. The former limitation is caused by stair-casing in the geometrical modelling, the latter by accumulated dispersion error throughout the mesh. The FEM can be seen as a general mathematical framework describing families of concrete numerical method implementations; in fact the FDTD can be described as a particular FETD (Finite Element Time Domain) method. To date the most commonly described FETD CEM methods make use of unstructured, conforming meshes and implicit time stepping schemes. Such meshes deal well with complex geometries while implicit time stepping is required for practical numerical stability. Compared to the FDTD, these methods have the advantages of computational efficiency when dealing with complex geometries and the conceptually straight forward extension to higher orders of accuracy. On the downside, they are much more complicated to implement and less computationally efficient when dealing with regular geometries. The FDTD and implicit FETD have been combined in an implicit/explicit hybrid. By using the implicit FETD in regions of complex geometry and the FDTD elsewhere the advantages of both are combined. However, previous work only addressed mixed first order (i.e. second order accurate) methods. For electrically large problems or when very accurate solutions are required, higher order methods are attractive. In this thesis a novel higher order implicit/explicit FETD method of arbitrary order in space is presented. A higher order explicit FETD method is implemented using Gauss-Lobatto lumping on regular Cartesian hexahedra with central differencing in time applied to a coupled Maxwell’s equation FEM formulation. This can be seen as a spatially higher order generalisation of the FDTD. A convolution-free perfectly matched layer (PML) method is adapted from the FDTD literature to provide mesh termination. A curl conforming hybrid mesh allowing the interconnection of arbitrary order tetrahedra and hexahedra without using intermediate pyramidal or prismatic elements is presented. An unconditionally stable implicit FETD method is implemented using Newmark-Beta time integration and the standard curl-curl FEM formulation. The implicit/explicit hybrid is constructed on the hybrid hexahedral/tetrahedral mesh using the equivalence between the coupled Maxwell’s formulation with central differences and the Newmark-Beta method with Beta = 0 and the element-wise implicitness method. The accuracy and efficiency of this hybrid is numerically demonstrated using several test-problems.
Baranda, Inok Antonio Filipe. "Investigation of high-order, high-resolution methods for axisymmetric turbulent jet usin ILEs." Thesis, Cranfield University, 2011. http://dspace.lib.cranfield.ac.uk/handle/1826/7317.
Full textBaranda, Inok Antonio Filipe. "Investigation of high-order, high-resolution methods for axisymmetric turbulent jet using ILEs." Thesis, Cranfield University, 2011. http://dspace.lib.cranfield.ac.uk/handle/1826/7317.
Full textEkelschot, Dirk. "Mesh adaptation strategies for compressible flows using a high-order spectral/hp element discretisation." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/43340.
Full textSherer, Scott Eric. "Investigation of high-order and optimized interpolation methods with implementation in a high-order overset grid fluid dynamics solver /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486462702465327.
Full textStoyanov, Miroslav. "Reduced Order Methods for Large Scale Riccati Equations." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/27832.
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Gargallo, Peiró Abel. "Validation and generation of curved meshes for high-order unstructured methods." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/275977.
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