Дисертації з теми "Discontinuous spectral element method"
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De, Grazia Daniele. "Three-dimensional discontinuous spectral/hp element methods for compressible flows." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/40416.
Повний текст джерелаCitrain, Aurélien. "Hybrid finite element methods for seismic wave simulation : coupling of discontinuous Galerkin and spectral element discretizations." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR28.
Повний текст джерелаTo solve wave equations in heterogeneous media with finite elements with a reasonable numerical cost, we couple the Discontinuous Galerkin method (DGm) with Spectral Elements method (SEm). We use hybrid meshes composed of tetrahedra and structured hexahedra. The coupling is carried out starting from a mixed-primal DG formulation applied on a hybrid mesh composed of a hexahedral macro-element and a sub-mesh composed of tetrahedra. The SEm is applied in the macro-element paved with structured hexahedrons and the coupling is ensured by the DGm numerical fluxes applied on the internal faces of the macro-element common with the tetrahedral mesh. The stability of the coupled method is demonstrated when time integration is performed with a Leap-Frog scheme. The performance of the coupled method is studied numerically and it is shown that the coupling reduces numerical costs while keeping a high level of accuracy. It is also shown that the coupled formulation can stabilize the DGm applied in areas that include Perfectly Matched Layers
Mengaldo, Gianmarco. "Discontinuous spectral/hp element methods : development, analysis and applications to compressible flows." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/28678.
Повний текст джерелаClaus, Susanne. "Numerical simulation of complex viscoelastic flows using discontinuous galerkin spectral/hp element methods." Thesis, Cardiff University, 2013. http://orca.cf.ac.uk/46909/.
Повний текст джерелаWintermeyer, Niklas [Verfasser], and Gregor [Gutachter] Gassner. "A novel entropy stable discontinuous Galerkin spectral element method for the shallow water equations on GPUs / Niklas Wintermeyer ; Gutachter: Gregor Gassner." Köln : Universitäts- und Stadtbibliothek Köln, 2019. http://d-nb.info/1182533183/34.
Повний текст джерелаVangelatos, Serena [Verfasser]. "On the Efficiency of Implicit Discontinuous Galerkin Spectral Element Methods for the Unsteady Compressible Navier-Stokes Equations / Serena Vangelatos." München : Verlag Dr. Hut, 2020. http://d-nb.info/1222352222/34.
Повний текст джерелаVangelatos, Serena [Verfasser], and Claus-Dieter [Akademischer Betreuer] Munz. "On the efficiency of implicit discontinuous Galerkin spectral element methods for the unsteady compressible Navier-Stokes equations / Serena Vangelatos ; Betreuer: Claus-Dieter Munz." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2020. http://d-nb.info/1206184051/34.
Повний текст джерелаSert, Cuneyt. "Nonconforming formulations with spectral element methods." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/1268.
Повний текст джерелаChaurasia, Hemant Kumar. "A time-spectral hybridizable discontinuous Galerkin method for periodic flow problems." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90647.
Повний текст джерелаCataloged from PDF version of thesis.
Includes bibliographical references (pages 110-120).
Numerical simulations of time-periodic flows are an essential design tool for a wide range of engineered systems, including jet engines, wind turbines and flapping wings. Conventional solvers for time-periodic flows are limited in accuracy and efficiency by the low-order Finite Volume and time-marching methods they typically employ. These methods introduce significant numerical dissipation in the simulated flow, and can require hundreds of timesteps to describe a periodic flow with only a few harmonic modes. However, recent developments in high-order methods and Fourier-based time discretizations present an opportunity to greatly improve computational performance. This thesis presents a novel Time-Spectral Hybridizable Discontinuous Galerkin (HDG) method for periodic flow problems, together with applications to flow through cascades and rotor/stator assemblies in aeronautical turbomachinery. The present work combines a Fourier-based Time-Spectral discretization in time with an HDG discretization in space, realizing the dual benefits of spectral accuracy in time and high-order accuracy in space. Low numerical dissipation and favorable stability properties are inherited from the high-order HDG method, together with a reduced number of globally coupled degrees of freedom compared to other DG methods. HDG provides a natural framework for treating boundary conditions, which is exploited in the development of a new high-order sliding mesh interface coupling technique for multiple-row turbomachinery problems. A regularization of the Spalart-Allmaras turbulence model is also employed to ensure numerical stability of unsteady flow solutions obtained with high-order methods. Turning to the temporal discretization, the Time-Spectral method enables direct solution of a periodic flow state, bypasses initial transient behavior, and can often deliver substantial savings in computational cost compared to implicit time-marching. An important driver of computational efficiency is the ability to select and resolve only the most important frequencies of a periodic problem, such as the blade-passing frequencies in turbomachinery flows. To this end, the present work introduces an adaptive frequency selection technique, using the Time-Spectral residual to form an inexpensive error indicator. Having selected a set of frequencies, the accuracy of the Time-Spectral solution is greatly improved by using optimally selected collocation points in time. For multi-domain problems such as turbomachinery flows, an anti-aliasing filter is also needed to avoid errors in the transfer of the solution across the sliding interface. All of these aspects contribute to the Adaptive Time-Spectral HDG method developed in this thesis. Performance characteristics of the method are demonstrated through applications to periodic ordinary differential equations, a convection problem, laminar flow over a pitching airfoil, and turbulent flow through a range of single- and multiple-row turbomachinery configurations. For a 2:1 rotor/stator flow problem, the Adaptive Time-Spectral HDG method correctly identifies the relevant frequencies in each blade row. This leads to an accurate periodic flow solution with greatly reduced computational cost, when compared to sequentially selected frequencies or a time-marching solution. For comparable accuracy in prediction of rotor loading, the Adaptive Time- Spectral HDG method incurs 3 times lower computational cost (CPU time) than time-marching, and for prediction of only the 1st harmonic amplitude, these savings rise to a factor of 200. Finally, in three-row compressor flow simulations, a high-order HDG method is shown to achieve significantly greater accuracy than a lower-order method with the same computational cost. For example, considering error in the amplitude of the 1st harmonic mode of total rotor loading, a p = 1 computation results in 20% error, in contrast to only 1% error in a p = 4 solution with comparable cost. This highlights the benefits that can be obtained from higher-order methods in the context of turbomachinery flow problems.
by Hemant Kumar Chaurasia.
Ph. D.
Bao, Weiyu. "Modelling excavations in discontinuous rock using the distinct element method." Thesis, University of Southampton, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.431928.
Повний текст джерелаLindley, Jorge Vicente Malik. "A discontinuous Galerkin finite element method for quasi-geostrophic frontogenesis." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/102632/.
Повний текст джерелаToolabi, Milad. "Dynamic extended finite element method (XFEM) analysis of discontinuous media." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/44180.
Повний текст джерелаGürkan, Ceren. "Extended hybridizable discontinuous Galerkin method." Doctoral thesis, Universitat Politècnica de Catalunya, 2018. http://hdl.handle.net/10803/664035.
Повний текст джерелаEsta tesis propone una nueva técnica numérica: eXtended Hybridizable Discontinuous Galerkin (X-HDG), para resolver eficazmente problemas incluyendo fronteras en movimiento e interfaces. Su objetivo es superar las limitaciones de los métodos disponibles y mejorar los resultados, heredando propiedades del método Hybridizable Discontinuous Galerkin method (HDG), junto con una definición de interfaz explícita. X-HDG combina el método HDG con la filosofía de eXtended Finite Element method (X-FEM), con una descripción level-set de la interfaz, para obtener un método numérico hp convergente de orden superior sin ajuste de la malla a la interfaz o frontera. HDG supera a otros métodos de DG para los problemas implícitos con operadores autoadjuntos, debido a sus propiedades de hibridación y superconvergencia. El proceso de hibridación reduce drásticamente el número de grados de libertad en el problema discreto, similar a la condensación estática en el contexto de Continuous Galerkin (CG) de alto orden. Por otro lado, HDG se basa en una formulación mixta que, a diferencia de CG u otros métodos DG, es estable incluso cuando todas las variables (incógnitas primitivas y derivadas) se aproximan con polinomios del mismo grado k. Como resultado, la convergencia de orden k + 1 en la norma L2 se demuestra no sólo para la incógnita primal sino también para sus derivadas. Por lo tanto, un simple post-proceso elemento-a-elemento de las derivadas conduce a una aproximación superconvergente de las variables primales, con convergencia de orden k+2 en la norma L2. X-HDG hereda estas propiedades. Por otro lado, gracias a la descripción level-set de la interfaz, se evita caro remallado tratando las interfaces móviles. Este trabajo demuestra que X-HDG mantiene la convergencia óptima y la superconvergencia de HDG sin la necesidad de ajustar la malla a la interfaz. En los capítulos 2 y 3, se deduce e implementa el método X-HDG para resolver la ecuación de Laplace estacionaria en un dominio donde la interfaz separa un solo material del vacío y donde la interfaz separa dos materiales diferentes. La precisión y convergencia de X-HDG se prueba con ejemplos de soluciones fabricadas y se demuestra que X-HDG supera las propuestas anteriores mostrando convergencia óptima y superconvergencia de alto orden, junto con una reducción del tamaño del sistema gracias a su naturaleza híbrida, pero sin ajuste de la malla. En los capítulos 4 y 5, el método X-HDG se desarrolla e implementa para resolver el problema de interfaz de Stokes para interfaces vacías y bimateriales. Con X-HDG, de nuevo se muestra una convergencia de alto orden en mallas no adaptadas, para problemas de flujo incompresible. X-HDG para interfaces móviles se discute en el Capítulo 6. Se considera un problema térmico transitorio, donde el término dependiente del tiempo es discretizado usando el método de backward Euler. Un ejemplo de una interfaz circulas que se reduce, junto con el problema de Stefan de dos fases, se discute en la sección de ejemplos numéricos. Se demuestra que X-HDG ofrece un alto grado de convergencia óptima para problemas dependientes del tiempo. Además, con el problema de Stefan, usando un grado polinomial k, se demuestra una aproximación más exacta de la posición de la interfaz contra X-FEM, gracias a la aproximación del gradiente convergente k + 1 de X-HDG. Una vez más, se mejoran los resultados obtenidos por las propuestas anteriores
Jeannequin, Nicolas. "Nodal Spectral Element Method Applied To Electrocardiological Models." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526068.
Повний текст джерелаMeng, Sha. "A spectral element method for viscoelastic fluid flow." Thesis, De Montfort University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369907.
Повний текст джерелаElfverson, Daniel. "Discontinuous Galerkin Multiscale Methods for Elliptic Problems." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-138960.
Повний текст джерелаMoura, Rodrigo Costa. "A high-order unstructured discontinuous galerkin finite element method for aerodynamics." Instituto Tecnológico de Aeronáutica, 2012. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2158.
Повний текст джерелаZheng, Yu. "Numerical simulation of droplet deformation using spectral element method." Thesis, Cardiff University, 2007. http://orca.cf.ac.uk/54648/.
Повний текст джерелаKocal, Arman. "Three Dimensional Numerical Modelling Of Discontinuous Rocks By Using Distinct Element Method." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12610005/index.pdf.
Повний текст джерела2 cases and Ç
an Lignite Establishment (Ç
Li). The results with the new model option, which allows users to use important discontinuity surface properties like joint roughness coefficient and joint wall compressive strength, compared well with results of previous studies using Mohr-Coulomb failure criterion.
Xiao, Yilong. "A Discontinuous Galerkin Finite Element Method Solution of One-Dimensional Richards’ Equation." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461255638.
Повний текст джерелаToutip, Wattana. "The dual reciprocity boundary element method for linear and non-linear problems." Thesis, University of Hertfordshire, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369302.
Повний текст джерелаJu, Xiaozhu. "A discontinuous transport methodology for solidification modelling." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/a-discontinuous-transport-methodology-for-solidification-modelling(32f86a90-05f6-45a1-938f-357e93398d39).html.
Повний текст джерелаHellwig, Friederike. "Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20034.
Повний текст джерелаThe thesis "Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods" proves optimal convergence rates for four lowest-order discontinuous Petrov-Galerkin methods for the Poisson model problem for a sufficiently small initial mesh-size in two different ways by equivalences to two other non-standard classes of finite element methods, the reduced mixed and the weighted Least-Squares method. The first is a mixed system of equations with first-order conforming Courant and nonconforming Crouzeix-Raviart functions. The second is a generalized Least-Squares formulation with a midpoint quadrature rule and weight functions. The thesis generalizes a result on the primal discontinuous Petrov-Galerkin method from [Carstensen, Bringmann, Hellwig, Wriggers 2018] and characterizes all four discontinuous Petrov-Galerkin methods simultaneously as particular instances of these methods. It establishes alternative reliable and efficient error estimators for both methods. A main accomplishment of this thesis is the proof of optimal convergence rates of the adaptive schemes in the axiomatic framework [Carstensen, Feischl, Page, Praetorius 2014]. The optimal convergence rates of the four discontinuous Petrov-Galerkin methods then follow as special cases from this rate-optimality. Numerical experiments verify the optimal convergence rates of both types of methods for different choices of parameters. Moreover, they complement the theory by a thorough comparison of both methods among each other and with their equivalent discontinuous Petrov-Galerkin schemes.
Dosopoulos, Stylianos. "Interior Penalty Discontinuous Galerkin Finite Element Method for the Time-Domain Maxwell's Equations." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337787922.
Повний текст джерелаBurleson, John Taylor. "Numerical Simulations of Viscoelastic Flows Using the Discontinuous Galerkin Method." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/104869.
Повний текст джерелаMaster of Science
Viscoelastic fluids are a type of non-Newtonian fluid of great importance to the study of fluid flows. Such fluids exhibit both viscous and elastic behaviors. We develop a numerical method to solve the partial differential equations governing viscoelastic fluid flows using various finite element methods. Our method is then validated using previous numerical results in literature.
Massey, Thomas Christopher. "A Flexible Galerkin Finite Element Method with an A Posteriori Discontinuous Finite Element Error Estimation for Hyperbolic Problems." Diss., Virginia Tech, 2002. http://hdl.handle.net/10919/28245.
Повний текст джерелаPh. D.
Harkin, Anthony. "A Legendre spectral element method for the rotational Navier-Stokes equations." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/37551.
Повний текст джерелаWessel, Richard Allen Jr. "Spectral element method for numerical simulation of unsteady laminar diffusion flames." Case Western Reserve University School of Graduate Studies / OhioLINK, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=case1057076472.
Повний текст джерелаOhlsson, Johan. "Spectral-element simulations of separated turbulent internal flows." Licentiate thesis, Stockholm : Skolan för teknikvetenskap, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11643.
Повний текст джерелаKlenow, Bradley. "Finite and Spectral Element Methods for Modeling Far-Field Underwater Explosion Effects on Ships." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/37648.
Повний текст джерелаPh. D.
Bailey, Teresa S. "The piecewise linear discontinuous finite element method applied to the RZ and XYZ transport equations." Diss., Texas A&M University, 2008. http://hdl.handle.net/1969.1/85942.
Повний текст джерелаVadsola, 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.
Повний текст джерелаKim, Bo Hung. "A graphical preprocessing interface for non-conforming spectral element solvers." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1819.
Повний текст джерелаVoonna, Kiran. "Development of discontinuous galerkin method for 1-D inviscid burgers equation." ScholarWorks@UNO, 2003. http://louisdl.louislibraries.org/u?/NOD,75.
Повний текст джерелаTitle from electronic submission form. "A thesis ... in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical Engineering"--Thesis t.p. Vita. Includes bibliographical references.
Taghaddosi, Farzad. "3D parallel computations of turbofan noise propagation using a spectral element method." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102733.
Повний текст джерелаDue to the special nature of acoustic wave propagation, the spatial discretization is performed using a spectral element method, where a tensor product of the nth-degree polynomials based on Chebyshev orthogonal functions is used to approximate variations within hexahedral elements. Non-reflecting boundary conditions are imposed at the far-field using a damping layer concept. This is done by augmenting the continuity equation with an additional term without modifying the governing equations as in PML methods.
Solution of the linear system of equations for the acoustic problem is based on the Schur complement method, which is a nonoverlapping domain decomposition technique. The Schur matrix is first solved using a matrix-free iterative method, whose convergence is accelerated with a novel local preconditioner. The solution in the entire domain is then obtained by finding solutions in smaller subdomains.
The 3D code also contains a mean flow solver based on the full potential equation in order to take into account the effects of flow variations around the nacelle on the scattering of the radiated sound field.
All aspects of numerical simulations, including building and assembling the coefficient matrices, implementation of the Schur complement method, and solution of the system of equations for both the acoustic and mean flow problems are performed on multiprocessors in parallel using the resources of the CLUMEQ Supercomputer Center. A large number of test cases are presented, ranging in size from 100 000-2 000 000 unknowns for which, depending on the size of the problem, between 8-48 CPU's are used.
The developed code is demonstrated to be robust and efficient in simulating acoustic propagation for a large number of problems, with an excellent parallel performance.
Bolis, Alessandro. "Fourier spectral/hp element method : investigation of time-stepping and parallelisation strategies." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/25140.
Повний текст джерелаCui, Xiaoming. "Discontinuous finite/boundary element method for radiative heat transfer with application in laser cancer therapy." Online access for everyone, 2005. http://www.dissertations.wsu.edu/Dissertations/Fall2005/x%5Fcui%5F121805.pdf.
Повний текст джерелаChoe, Kyu Y. "The discontinuous finite element method with the Taylor-Galerkin approach for nonlinear hyperbolic conservation laws /." Thesis, Connect to this title online; UW restricted, 1991. http://hdl.handle.net/1773/9977.
Повний текст джерелаQuattrochi, Douglas J. (Douglas John). "Hypersonic heat transfer and anisotropic visualization with a higher order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/35567.
Повний текст джерелаIncludes bibliographical references (leaves 83-89).
Higher order discretizations of the Navier-Stokes equations promise greater accuracy than conventional computational aerodynamics methods. In particular, the discontinuous Galerkin (DG) finite element method has O(hP+l) design accuracy and allows for subcell resolution of shocks. This work furthers the DG finite element method in two ways. First, it demonstrates the results of DG when used to predict heat transfer to a cylinder in a hypersonic flow. The strong shock is captured with a Laplacian artificial viscosity term. On average, the results are in agreement with an existing hypersonic benchmark. Second, this work improves the visualization of the higher order polynomial solutions generated by DG with an adaptive display algorithm. The new algorithm results in more efficient displays of higher order solutions, including the hypersonic flow solutions generated here.
by Douglas J. Quattrochi.
S.M.
Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.
Повний текст джерелаLa implementació i aplicació de NEFEM a problemes que requereixen una descripció acurada del contorn són, també, objectius prioritaris d'aquesta tesi. Per exemple, la solució numèrica de les equacions de Maxwell és molt sensible a la descripció geomètrica. Es presenta l'aplicació de NEFEM a problemes d'scattering d'ones electromagnètiques amb una formulació de Galerkin discontinu. S'investiga l'habilitat de NEFEM per obtenir solucions precises amb malles grolleres i aproximacions d'alt ordre, i s'exploren les possibilitats de les anomenades malles NEFEM, amb elements que contenen singularitats dintre d'una cara o aresta d'un element. Utilitzant NEFEM, la mida de la malla no està controlada per la complexitat de la geometria. Això implica una dràstica diferència en la mida dels elements i, per tant, suposa un gran estalvi tant des del punt de vista de requeriments de memòria com de cost computacional. Per tant, NEFEM és una eina poderosa per la simulació de problemes tridimensionals a gran escala amb geometries complexes. D'altra banda, la simulació de problemes d'scattering d'ones electromagnètiques requereix mecanismes per aconseguir una absorció eficient de les ones scattered. En aquesta tesi es discuteixen, optimitzen i comparen dues tècniques en el context de mètodes de Galerkin discontinu amb aproximacions d'alt ordre.
La resolució numèrica de les equacions d'Euler de la dinàmica de gasos és també molt sensible a la representació geomètrica. Quan es considera una formulació de Galerkin discontinu i elements isoparamètrics lineals, una producció espúria d'entropia pot evitar la convergència cap a la solució correcta. Amb NEFEM, l'acurada imposició de la condició de contorn en contorns impenetrables proporciona resultats precisos inclús amb una aproximació lineal de la solució. A més, la representació exacta del contorn permet una imposició adequada de les condicions de contorn amb malles grolleres i graus d'interpolació alts. Una propietat atractiva de la implementació proposada és que moltes de les rutines usuals en un codi d'elements finits poden ser aprofitades, per exemple rutines per realitzar el càlcul de les matrius elementals, assemblatge, etc. Només és necessari implementar noves rutines per calcular les quadratures numèriques en elements corbs i emmagatzemar el valor de les funciones de forma en els punts d'integració. S'han proposat vàries tècniques d'elements finits corbs a la literatura. En aquesta tesi, es compara NEFEM amb altres tècniques populars d'elements finits corbs (isoparamètics, cartesians i p-FEM), des de tres punts de vista diferents: aspectes teòrics, implementació i eficiència numèrica. En els exemples numèrics, NEFEM és, com a mínim, un ordre de magnitud més precís comparat amb altres tècniques. A més, per una precisió desitjada NEFEM és també més eficient: necessita un 50% dels graus de llibertat que fan servir els elements isoparamètrics o p-FEM per aconseguir la mateixa precisió. Per tant, l'ús de NEFEM és altament recomanable en presència de contorns corbs i/o quan el contorn té detalls geomètrics complexes.
This thesis proposes an improvement of the classical finite element method (FEM) for an efficient treatment of curved boundaries: the NURBSenhanced FEM (NEFEM). It is able to exactly represent the geometry by means of the usual CAD boundary representation with non-uniform rational Bsplines (NURBS), while the solution is approximated with a standard piecewise polynomial interpolation. Therefore, in the vast majority of the domain, interpolation and numerical integration are standard, preserving the classical finite element (FE) convergence properties, and allowing a seamless coupling with standard FEs on the domain interior. Specifically designed polynomial interpolation and numerical integration are designed only for those elements affected by the NURBS boundary representation.
The implementation and application of NEFEM to problems demanding an accurate boundary representation are also primary goals of this thesis. For instance, the numerical solution of Maxwell's equations is highly sensitive to geometry description. The application of NEFEM to electromagnetic scattering problems using a discontinuous Galerkin formulation is presented. The ability of NEFEM to compute an accurate solution with coarse meshes and high-order approximations is investigated, and the possibilities of NEFEM meshes, with elements containing edge or corner singularities, are explored. With NEFEM, the mesh size is no longer subsidiary to geometry complexity, and depends only on the accuracy requirements on the solution, whereas standard FEs require mesh refinement to properly capture the geometry. This implies a drastic difference in mesh size that results in drastic memory savings, and also important savings in computational cost. Thus, NEFEM is a powerful tool for large-scale scattering simulations with complex geometries in three dimensions. Another key issue in the numerical solution of electromagnetic scattering problems is using a mechanism to perform the absorption of outgoing waves. Two perfectly matched layers are discussed, optimized and compared in a high-order discontinuous Galerkin framework.
The numerical solution of Euler equations of gas dynamics is also very sensitive to geometry description. Using a discontinuous Galerkin formulation and linear isoparametric elements, a spurious entropy production may prevent convergence to the correct solution. With NEFEM, the exact imposition of the solid wall boundary condition provides accurate results even with a linear approximation of the solution. Furthermore, the exact boundary representation allows using coarse meshes, but ensuring the proper implementation of the solid wall boundary condition. An attractive feature of the proposed implementation is that the usual routines of a standard FE code can be directly used, namely routines for the computation of elemental matrices and vectors, assembly, etc. It is only necessary to implement new routines for the computation of numerical quadratures in curved elements and to store the value of shape functions at integration points.
Several curved FE techniques have been proposed in the literature. In this thesis, NEFEM is compared with some popular curved FE techniques (namely isoparametric FEs, cartesian FEs and p-FEM), from three different perspectives: theoretical aspects, implementation and performance. In every example shown, NEFEM is at least one order of magnitude more accurate compared to other techniques. Moreover, for a desired accuracy NEFEM is also computationally more efficient. In some examples, NEFEM needs only 50% of the number of degrees of freedom required by isoparametric FEs or p-FEM. Thus, the use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details.
Storn, Johannes. "Topics in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Analysis." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20141.
Повний текст джерелаThe analysis of partial differential equations is a core area in mathematics due to the fundamental role of partial differential equations in the description of phenomena in applied sciences. Computers can approximate the solutions to these equations for many problems. They use numerical schemes which should provide good approximations and verify the accuracy. The least-squares finite element method (LSFEM) and the discontinuous Petrov-Galerkin (DPG) method satisfy these requirements. This thesis investigates these two schemes. The first part of this thesis explores the accuracy of solutions to the LSFEM. It combines properties of the underlying partial differential equation with properties of the LSFEM and so proves the asymptotic equality of the error and a computable residual. Moreover, this thesis introduces an novel scheme for the computation of guaranteed upper error bounds. While the established error estimator leads to a significant overestimation of the error, numerical experiments indicate a tiny overestimation with the novel bound. The investigation of error bounds for the Stokes problem visualizes a relation of the LSFEM and the Ladyzhenskaya-Babuška-Brezzi (LBB) constant. This constant is a key in the existence and stability of solution to problems in fluid dynamics. The second part of this thesis utilizes this relation to design a competitive numerical scheme for the computation of the LBB constant. The third part of this thesis investigates the DPG method. It analyses an abstract framework which compiles existing applications of the DPG method. The analysis relates the DPG method with a slightly perturbed LSFEM. Hence, the results from the first part of this thesis extend to the DPG method. This enables a precise investigation of existing and the design of novel DPG schemes.
Lu, James 1977. "An a posteriori error control framework for adaptive precision optimization using discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/34134.
Повний текст джерелаIncludes bibliographical references (leaves 169-178).
Introduction: Aerodynamic design optimization has seen significant development over the past decade. Adjoint-based shape design for elliptic systems was first proposed by Pironneau and applied to transonic flow by Jameson . A review of the aerodynamic shape optimization literature and a large list of references is given in. Over the years much technology has been developed, allowing engineers to contemplate applying optimization methods to a wide variety of problems. In the context of structured grids, adjoint-based applications include multipoint, multi-objective airfoil design using compressible Navier-Stokes equations and 3D multipoint design of aircraft configurations using inviscid Euler equations. There have also been significant effort in applying adjoint methods to the unstructured grid setting. In this context, Newman et al., Elliot and Peraire were among the first to develop discrete adjoint approaches for the inviscid Euler equations.
by James Ching-Chi
Ph.D.
Oliver, Todd A. 1980. "A high-order, adaptive, discontinuous Galerkin finite element method for the Reynolds-Averaged Navier-Stokes equations." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/46818.
Повний текст джерелаThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 175-182).
This thesis presents high-order, discontinuous Galerkin (DG) discretizations of the Reynolds-Averaged Navier-Stokes (RANS) equations and an output-based error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the Spalart-Allmaras (SA) turbulence model are examined. The dual consistency of multiple DG discretizations of the RANS-SA system is analyzed. The approach of simply weighting gradient dependent source terms by a test function and integrating is shown to be dual inconsistent. A dual consistency correction for this discretization is derived. The analysis also demonstrates that discretizations based on the popular mixed formulation, where dependence on the state gradient is handled by introducing additional state variables, are generally asymptotically dual consistent. Numerical results are presented to confirm the results of the analysis. The output error estimation and output-based adaptation algorithms used here are extensions of methods previously developed in the finite volume and finite element communities. In particular, the methods are extended for application on the curved, highly anisotropic meshes required for boundary conforming, high-order RANS simulations. Two methods for generating such curved meshes are demonstrated. One relies on a user-defined global mapping of the physical domain to a straight meshing domain. The other uses a linear elasticity node movement scheme to add curvature to an initially linear mesh. Finally, to improve the robustness of the adaptation process, an "unsteady" algorithm, where the mesh is adapted at each time step, is presented. The goal of the unsteady procedure is to allow mesh adaptation prior to converging a steady state solution, not to obtain a time-accurate solution of an unsteady problem. Thus, an estimate of the error due to spatial discretization in the output of interest averaged over the current time step is developed. This error estimate is then used to drive an h-adaptation algorithm. Adaptation results demonstrate that the high-order discretizations are more efficient than the second-order method in terms of degrees of freedom required to achieve a desired error tolerance. Furthermore, using the unsteady adaptation process, adaptive RANS simulations may be started from extremely coarse meshes, significantly decreasing the mesh generation burden to the user.
by Todd A. Oliver.
Ph.D.
Oliver, Todd A. "A High-Order, Adaptive, Discontinuous Galerkin Finite Element Method for the Reynolds-Averaged Navier-Stokes Equations." Ft. Belvoir : Defense Technical Information Center, 2008. http://handle.dtic.mil/100.2/ADA488912.
Повний текст джерелаPiatkowski, Stephan-Marian [Verfasser], and Peter [Akademischer Betreuer] Bastian. "A Spectral Discontinuous Galerkin method for incompressible flow with Applications to turbulence / Stephan-Marian Piatkowski ; Betreuer: Peter Bastian." Heidelberg : Universitätsbibliothek Heidelberg, 2019. http://d-nb.info/1191760529/34.
Повний текст джерелаBirgersson, Fredrik. "Prediction of random vibration using spectral methods." Doctoral thesis, KTH, Aeronautical and Vehicle Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3694.
Повний текст джерелаMuch of the vibration in fast moving vehicles is caused bydistributed random excitation, such as turbulent flow and roadroughness. Piping systems transporting fast flowing fluid isanother example, where distributed random excitation will causeunwanted vibration. In order to reduce these vibrations andalso the noise they cause, it is important to have accurate andcomputationally efficient prediction methods available.
The aim of this thesis is to present such a method. Thefirst step towards this end was to extend an existing spectralfinite element method (SFEM) to handle excitation of planetravelling pressure waves. Once the elementary response tothese waves is known, the response to arbitrary homogeneousrandom excitation can be found.
One example of random excitation is turbulent boundary layer(TBL) excitation. From measurements a new modified Chase modelwas developed that allowed for a satisfactory prediction ofboth the measured wall pressure field and the vibrationresponse of a turbulence excited plate. In order to model morecomplicated structures, a new spectral super element method(SSEM) was formulated. It is based on a waveguide formulation,handles all kinds of boundaries and its elements are easily putinto an assembly with conventional finite elements.
Finally, the work to model fluid-structure interaction withanother wave based method is presented. Similar to the previousmethods it seems to be computationally more efficient thanconventional finite elements.
Nappi, Angela. "Development and Application of a Discontinuous Galerkin-based Wave Prediction Model." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385998191.
Повний текст джерелаAlpert, David N. "Enriched Space-Time Finite Element Methods for Structural Dynamics Applications." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870451.
Повний текст джерелаBarter, Garrett E. (Garrett Ehud) 1979. "Shock capturing with PDE-based artificial viscosity for an adaptive, higher-order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44931.
Повний текст джерелаThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 135-143).
The accurate simulation of supersonic and hypersonic flows is well suited to higher-order (p > 1), adaptive computational fluid dynamics (CFD). Since these cases involve flow velocities greater than the speed of sound, an appropriate shock capturing for higher-order, adaptive methods is necessary. Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a nonsmooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficulties, this work proposes a new, higher-order, state based artificial viscosity with an associated governing partial differential equation (PDE). In the governing PDE, the shock sensor acts as a forcing term, driving the artificial viscosity to a non-zero value where it is necessary. The decay rate of the higher-order solution modes and edge-based jumps are both shown to be reliable shock indicators. This new approach leads to a smooth, higher-order representation of the artificial viscosity that evolves in time with the solution. For applications involving the Navier-Stokes equations, an artificial dissipation operator that preserves total enthalpy is introduced. The combination of higher-order, PDE-based artificial viscosity and enthalpy-preserving dissipation operator is shown to overcome the disadvantages of the non-smooth artificial viscosity. The PDE-based artificial viscosity can be used in conjunction with an automated grid adaptation framework that minimizes the error of an output functional. Higher-order solutions are shown to reach strict engineering tolerances with fewer degrees of freedom.
(cont.) The benefit in computational efficiency for higher-order solutions is less dramatic in the vicinity of the shock where errors scale with O(h/p). This includes the near-field pressure signals necessary for sonic boom prediction. When applied to heat transfer prediction on unstructured meshes in hypersonic flows, the PDE-based artificial viscosity is less susceptible to errors introduced by poor shock-grid alignment. Surface heating can also drive the output-based grid adaptation framework to arrive at the same heat transfer distribution as a well-designed structured mesh.
by Garrett Ehud Barter.
Ph.D.
Akdag, Osman. "Incompressible Flow Simulations Using Least Squares Spectral Element Method On Adaptively Refined Triangular Grids." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614944/index.pdf.
Повний текст джерела