Spectral/hp element methods: recent developments, applications, and perspectives

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate C0-continuous expansions. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed

Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity

Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV).Peer ReviewedPostprint (author's final draft

A stabilized finite element method for the mixed wave equation in an ALE framework with application to diphthong production

The archived file is not the final published version of the article. © (2016) S. Hirzel Verlag/European Acoustics Association The definitive publisher-authenticated version is available online at http://www.ingentaconnect.com/contentone/dav/aaua/2016/00000102/00000001/art00012 Readers must contact the publisher for reprint or permission to use the material in any form.Working with the wave equation in mixed rather than irreducible form allows one to directly account for both, the acoustic pressure field and the acoustic particle velocity field. Indeed, this becomes the natural option in many problems, such as those involving waves propagating in moving domains, because the equations can easily be set in an arbitrary Lagrangian-Eulerian (ALE) frame of reference. Yet, when attempting a standard Galerkin finite element solution (FEM) for them, it turns out that an inf-sup compatibility constraint has to be satisfied, which prevents from using equal interpolations for the approximated acoustic pressure and velocity fields. In this work it is proposed to resort to a subgrid scale stabilization strategy to circumvent this condition and thus facilitate code implementation. As a possible application, we address the generation of diphthongs in voice production.Peer ReviewedPostprint (author's final draft

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described

Modelling Seismic Wave Propagation for Geophysical Imaging

International audienceThe Earth is an heterogeneous complex media from the mineral composition scale (10−6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Günther et al., 2006; Rücker et al., 2006), diffusive methods (Cognon, 1971; Druskin & Knizhnerman, 1988; Goldman & Stover, 1983; Hohmann, 1988; Kuo & Cho, 1980; Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968; Bolt & Smith, 1976; Dablain, 1986; Kelly et al., 1976; Levander, 1988; Marfurt, 1984; Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields

Simulation of flows with violent free surface motion and moving objects using unstructured grids

This is the peer reviewed version of the following article: [Löhner, R. , Yang, C. and Oñate, E. (2007), Simulation of flows with violent free surface motion and moving objects using unstructured grids. Int. J. Numer. Meth. Fluids, 53: 1315-1338. doi:10.1002/fld.1244], which has been published in final form at https://doi.org/10.1002/fld.1244. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.Peer ReviewedPostprint (author's final draft

Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation

Among the many additive manufacturing (AM) processes for metallic materials, selective laser melting (SLM) is arguably the most versatile in terms of its potential to realize complex geometries along with tailored microstructure. However, the complexity of the SLM process, and the need for predictive relation of powder and process parameters to the part properties, demands further development of computational and experimental methods. This review addresses the fundamental physical phenomena of SLM, with a special emphasis on the associated thermal behavior. Simulation and experimental methods are discussed according to three primary categories. First, macroscopic approaches aim to answer questions at the component level and consider for example the determination of residual stresses or dimensional distortion effects prevalent in SLM. Second, mesoscopic approaches focus on the detection of defects such as excessive surface roughness, residual porosity or inclusions that occur at the mesoscopic length scale of individual powder particles. Third, microscopic approaches investigate the metallurgical microstructure evolution resulting from the high temperature gradients and extreme heating and cooling rates induced by the SLM process. Consideration of physical phenomena on all of these three length scales is mandatory to establish the understanding needed to realize high part quality in many applications, and to fully exploit the potential of SLM and related metal AM processes

Signal and power integrity co-simulation using the multi-layer finite difference method

Mixed signal system-on-package (SoP) technology is a key enabler for increasing functional integration, especially in mobile and wireless systems. Due to the presence of multiple dissimilar modules, each having unique power supply requirements, the design of the power distribution network (PDN) becomes critical. Typically, this PDN is designed as alternating layers of power and ground planes with signal interconnects routed in between or on top of the planes. The goal for the simulation of multi-layer power/ground planes, is the following: Given a stack-up and other geometrical information, it is required to find the network parameters (S/Y/Z) between port locations. Commercial packages have extremely complicated stack-ups, and the trend to increasing integration at the package level only points to increasing complexity. It is computationally intractable to solve these problems using these existing methods. The approach proposed in this thesis for obtaining the response of the PDN is the multi-layer finite difference method (M-FDM). A surface mesh / finite difference based approach is developed, which leads to a system matrix that is sparse and banded, and can be solved efficiently. The contributions of this research are the following: 1. The development of a PDN modeler for multi-layer packages and boards called the the multi-layer finite difference method. 2. The enhancement of M-FDM using multi-port connection networks to include the effect of fringe fields and gap coupling. 3. An adaptive triangular mesh based scheme called the multi-layer finite element method (MFEM) to address the limitations of M-FDM 4. The use of modal decomposition for the co-simulation of signal nets with the PDN. 5. The use of a robust GA-based optimizer for the selection and placement of decoupling capacitors in multi-layer geometries. 6. Implementation of these methods in a tool called MSDT 1.Ph.D.Committee Chair: Madhavan Swaminathan; Committee Member: Andrew F. Peterson; Committee Member: David C. Keezer; Committee Member: Saibal Mukhopadyay; Committee Member: Suresh Sitarama

Numerical simulation of aeroacoustics using the variational multiscale method : application to the problem of human phonation

The solution of the human phonation problem applying computational mechanics is covered by several research branches, such as Computational Fluid Dynamics (CFD), biomechanics or acoustics, among others. In the present thesis, the problem is approached from the Computational Aeroacoustics (CAA) point of view and the first main objective consists in developing numerical methods of general application that can take part in the solution of any scenario related to human phonation with a reasonable cost. In this sense, only the compressible Navier-Stokes equations can describe all flow and acoustic scales without any modeling, which is known as Direct Numerical Simulation (DNS), but its computational cost is usually unaffordable. Even in the case of a Large Eddy Simulation (LES), where the small scales are modeled, the cost can still be a handicap due to the complexity of the problem. This drawback gets worse in the low Mach regime due to the large disparity between flow velocity and sound speed, which leads to an ill-conditioning of the system of equations, specially for conservative schemes. At this point, it makes sense to move towards the incompressible flow approximation, bearing in mind the low velocities expected in human phonation problems. Incompressible flows do not yield any acoustics, for which a second problem containing the propagation of the sound sources needs to be modeled and solved. These are the so called hybrid methods, which allow a better conditioning of the problem by segregating flow and acoustic scales. Lighthill's analogy has been taken as starting point for the present work, but its restriction to free-field scenarios has motivated the extension of the method to arbitrary geometries and non-uniform flows. The first development in this direction consists in a splitting of Lighthill's analogy into a quadrupolar and dipolar component, which does not change the original problem but allows assessing the contribution of solid boundaries to the generation of sound. The second step consists in the development of a stabilized Finite Element (FEM) formulation for the Acoustic Perturbation Equations (APE) which account for non-uniform flows and perform a complete filtering of the acoustic scales. The final step assumes the compressible approach but omitting the energy equation and thus considering both flow and acoustic propagation as isentropic. In this case the solver is unified and hence a method for applying compatible boundary conditions for flow and acoustics has been developed. Moreover, the whole numerical framework has been extended to dynamic phonation cases, which require using an Arbitrary Lagrangian Eulerian (ALE) reference. Also, a novel remeshing strategy with conservative interpolation between meshes is presented. In the last chapter a challenging case in human phonation has been chosen for testing the developed computational framework: the fricative phoneme /s/. Unlike vowels, which are voiced sounds defined by a few characteristic frequencies, fricatives cannot be simulated as the propagation of a known analytic solution (glottal pulse) because the sound sources correspond to a wide range of turbulent scales. Therefore, a CFD calculation is mandatory in order to capture all relevant eddies behind the generation of sound. This problem is solved with an LES together with the Variational Multiscale (VMS) stabilization method as turbulence model, which is supplemented with several acoustic formulations when using incompressible flow. The analysis of the results focuses on the numerical representation of turbulence and the acoustic signal at the far-field, which has been compared to experimental recordings. Finally, the role of the upper incisors in the generation of the fricative sound has been evaluated. All simulations have been run with the parallel multiphysics FEM code FEMUSS, based on FORTRAN Object-Oriented-Programming land the OpenMPI parallel library.La solució del problema de la veu humana des de la mecànica computacional és objecte d'estudi per part de diverses disciplines, com per exemple la Dinàmica de Fluids Computacional (CFD), la biomecànica o l'acústica. En la present tesi s'encara el problema des de l'Aeroacústica Computacional (CAA) i el primer objectiu consisteix en desenvolupar mètodes numèrics d'aplicació general que puguin ser part de la solució, amb un cost computacional raonable, de qualsevol escenari relacionat amb la fonació humana. En aquest sentit, només les equacions de flux compressible de Navier-Stokes aconsegueixen descriure totes les escales alhora, tant les dinàmiques com les acústiques, sense recórrer a cap modelització, conegut com a Simulació Numèrica Directa (DNS), però el seu cost computacional és normalment inassumible. Fins i tot en el cas d'una Large Eddy Simulation (LES), on les escales petites són modelades, el cost pot resultar excessiu a causa de la complexitat del problema. Aquest fet encara és més accentuat en el règim de baix nombre de Mach donada la gran disparitat entre la velocitat del fluid i la del so i el conseqüent mal condicionament del sistema d'equacions, sobretot en esquemes conservatius. Per tant, tenint en compte les baixes velocitats de l'aire al tracte vocal, té sentit recórrer a l'aproximació de flux incompressible. Els fluids incompressibles no inclouen la part acústica, de manera que cal calcular un segon problema que descrigui la propagació de les fonts de so. Aquests són els anomenats mètodes híbrids, que permeten un millor condicionament del problema gràcies a la segregació de les escales acústiques de les dinàmiques. S'ha pres l'analogia de Lighthill com a punt de partida, però la seva restricció a casos en camp obert ha motivat l'extensió del mètode cap a geometries arbitràries i fluxos no uniformes. El primer desenvolupament en aquesta direcció consisteix en la divisió de l'analogia de Lighthill en una component quadrupolar i una altra de dipolar, fet que no altera el problema original però que permet analitzar la contribució de cossos sòlids en la generació de so. El segon pas consisteix en el desenvolupament d'una formulació estabilitzada en elements finits (FEM) de les Acoustic Perturbation Equations (APE), que incorporen la propagació en fluxos no uniformes i que realitzen un filtrat complet de les escales acústiques. El pas final assumeix la compressibilitat del fluid però omet l'equació d'energia, i per tant considera la dinàmica i l'acústica fenòmens isentròpics. En aquest cas el solver és unificat i per tant s'ha desenvolupat un mètode per imposar condicions de contorn compatibles entre ambdues escales del fluid. Finalment, les formulacions numèriques han estat adaptades a casos de fonació dinàmica mitjançant una referència Arbitrària Lagrangiana Euleriana (ALE). A més, es presenta una estratègia de remallat amb interpolació conservativa entre malles. En l'últim capítol es presenta un cas de fonació humana que suposa un repte per la seva complexitat i que ha servit per validar les formulacions numèriques presentades: la fricativa sorda /s/. A diferència de les vocals, que són sons sonors definits per unes poques freqüències característiques, les fricatives no poden ser simulades com la propagació d'una funció analítica coneguda (pols glotal) perquè les fonts de so corresponen a un rang ampli d'escales turbulents. Per tant és necessària una simulació CFD per tal de capturar-les. El problema se soluciona amb un model de turbulència LES amb el mètode d'estabilització Variational Multiscale. L'anàlisi se centra en la representació numèrica de la turbulència i en el senyal acústic al camp llunyà, tot comparant-lo amb dades experimentals. Finalment, s'avalua la contribució dels incisius superiors en la generació del so fricatiu sord /s/. Totes les simulacions han estat realitzades amb el codi FEM multi-físic en paral·lel FEMUSS, basat en programació orientada a objectes en FORTRAN i en OpenMPI