258 research outputs found
On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations
The present paper deals with the numerical solution of the incompressible
Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods
for discretization in space. For DG methods applied to the dual splitting
projection method, instabilities have recently been reported that occur for
coarse spatial resolutions and small time step sizes. By means of numerical
investigation we give evidence that these instabilities are related to the
discontinuous Galerkin formulation of the velocity divergence term and the
pressure gradient term that couple velocity and pressure. Integration by parts
of these terms with a suitable definition of boundary conditions is required in
order to obtain a stable and robust method. Since the intermediate velocity
field does not fulfill the boundary conditions prescribed for the velocity, a
consistent boundary condition is derived from the convective step of the dual
splitting scheme to ensure high-order accuracy with respect to the temporal
discretization. This new formulation is stable in the limit of small time steps
for both equal-order and mixed-order polynomial approximations. Although the
dual splitting scheme itself includes inf-sup stabilizing contributions, we
demonstrate that spurious pressure oscillations appear for equal-order
polynomials and small time steps highlighting the necessity to consider inf-sup
stability explicitly.Comment: 31 page
A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
We present an efficient discontinuous Galerkin scheme for simulation of the
incompressible Navier-Stokes equations including laminar and turbulent flow. We
consider a semi-explicit high-order velocity-correction method for time
integration as well as nodal equal-order discretizations for velocity and
pressure. The non-linear convective term is treated explicitly while a linear
system is solved for the pressure Poisson equation and the viscous term. The
key feature of our solver is a consistent penalty term reducing the local
divergence error in order to overcome recently reported instabilities in
spatially under-resolved high-Reynolds-number flows as well as small time
steps. This penalty method is similar to the grad-div stabilization widely used
in continuous finite elements. We further review and compare our method to
several other techniques recently proposed in literature to stabilize the
method for such flow configurations. The solver is specifically designed for
large-scale computations through matrix-free linear solvers including efficient
preconditioning strategies and tensor-product elements, which have allowed us
to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores.
We validate our code and demonstrate optimal convergence rates with laminar
flows present in a vortex problem and flow past a cylinder and show
applicability of our solver to direct numerical simulation as well as implicit
large-eddy simulation of turbulent channel flow at as well as
.Comment: 28 pages, in preparation for submission to Journal of Computational
Physic
Nominal marking in Northern Tshwa (Kalahari Khoe)
Languages of the Khoe family have a complex pronominal system that distinguishes three categories each for person, gender, and number. However, while languages of the Khoekhoe branch and the western subgroup of Kalahari Khoe obligatorily or optionally mark nouns and nominal classifiers for gender and number, the nominal marking system in eastern Kalahari Khoe appears to be undergoing serious reduction. This article discusses data on personal pronouns and nominal gender-number marking in four little-known Northern Tshwa varieties, including data from Tjwao, a severely endangered language spoken by fewer than ten individuals in western Zimbabwe. We analyse personal pronoun use, case distinctions and nominal marking, focussing on characterising features and commonalities shared across the cluster. Our findings show a high degree of uniformity within Northern Tshwa, and at the same time suggest a more complex nominal marking system than was previously assumed for varieties of the Eastern Kalahari Khoe subgroup
A cross-linguistic database of phonetic transcription systems
Contrary to what non-practitioners might expect, the systems of phonetic notation used by linguists are highly idiosyncratic. Not only do various linguistic subfields disagree on the specific symbols they use to denote the speech sounds of languages, but also in large databases of sound inventories considerable variation can be found. Inspired by recent efforts to link cross-linguistic data with help of reference catalogues (Glottolog, Concepticon) across different resources, we present initial efforts to link different phonetic notation systems to a catalogue of speech sounds. This is achieved with the help of a database accompanied by a software framework that uses a limited but easily extendable set of non-binary feature values to allow for quick and convenient registration of different transcription systems, while at the same time linking to additional datasets with restricted inventories. Linking different transcription systems enables us to conveniently translate between different phonetic transcription systems, while linking sounds to databases allows users quick access to various kinds of metadata, including feature values, statistics on phoneme inventories, and information on prosody and sound classes. In order to prove the feasibility of this enterprise, we supplement an initial version of our cross-linguistic database of phonetic transcription systems (CLTS), which currently registers five transcription systems and links to fifteen datasets, as well as a web application, which permits users to conveniently test the power of the automatic translation across transcription systems
Efficiency of high-performance discontinuous Galerkin spectral element methods for under-resolved turbulent incompressible flows
The present paper addresses the numerical solution of turbulent flows with
high-order discontinuous Galerkin methods for discretizing the incompressible
Navier-Stokes equations. The efficiency of high-order methods when applied to
under-resolved problems is an open issue in literature. This topic is carefully
investigated in the present work by the example of the 3D Taylor-Green vortex
problem. Our implementation is based on a generic high-performance framework
for matrix-free evaluation of finite element operators with one of the best
realizations currently known. We present a methodology to systematically
analyze the efficiency of the incompressible Navier-Stokes solver for high
polynomial degrees. Due to the absence of optimal rates of convergence in the
under-resolved regime, our results reveal that demonstrating improved
efficiency of high-order methods is a challenging task and that optimal
computational complexity of solvers, preconditioners, and matrix-free
implementations are necessary ingredients to achieve the goal of better
solution quality at the same computational costs already for a geometrically
simple problem such as the Taylor-Green vortex. Although the analysis is
performed for a Cartesian geometry, our approach is generic and can be applied
to arbitrary geometries. We present excellent performance numbers on modern,
cache-based computer architectures achieving a throughput for operator
evaluation of 3e8 up to 1e9 DoFs/sec on one Intel Haswell node with 28 cores.
Compared to performance results published within the last 5 years for
high-order DG discretizations of the compressible Navier-Stokes equations, our
approach reduces computational costs by more than one order of magnitude for
the same setup
Robust and efficient discontinuous Galerkin methods for under-resolved turbulent incompressible flows
We present a robust and accurate discretization approach for incompressible
turbulent flows based on high-order discontinuous Galerkin methods. The DG
discretization of the incompressible Navier-Stokes equations uses the local
Lax-Friedrichs flux for the convective term, the symmetric interior penalty
method for the viscous term, and central fluxes for the velocity-pressure
coupling terms. Stability of the discretization approach for under-resolved,
turbulent flow problems is realized by a purely numerical stabilization
approach. Consistent penalty terms that enforce the incompressibility
constraint as well as inter-element continuity of the velocity field in a weak
sense render the numerical method a robust discretization scheme in the
under-resolved regime. The penalty parameters are derived by means of
dimensional analysis using penalty factors of order 1. Applying these penalty
terms in a postprocessing step leads to an efficient solution algorithm for
turbulent flows. The proposed approach is applicable independently of the
solution strategy used to solve the incompressible Navier-Stokes equations,
i.e., it can be used for both projection-type solution methods as well as
monolithic solution approaches. Since our approach is based on consistent
penalty terms, it is by definition generic and provides optimal rates of
convergence when applied to laminar flow problems. Robustness and accuracy are
verified for the Orr-Sommerfeld stability problem, the Taylor-Green vortex
problem, and turbulent channel flow. Moreover, the accuracy of high-order
discretizations as compared to low-order discretizations is investigated for
these flow problems. A comparison to state-of-the-art computational approaches
for large-eddy simulation indicates that the proposed methods are highly
attractive components for turbulent flow solvers
Model-driven software engineering for construction engineering: Quo vadis?
Models are an inherent part of the construction industry, which leverages from the steady advancements in information and communication technology. One of these advancements is Building Information Modeling (BIM), which denotes the move from 2D drawings to having semantically rich models of the objects subject to construction. Additionally, the way stakeholders collaborate in construction projects and their organization is revisited. This is commonly denoted as Integrated Project Delivery (IPD). Both BIM and IPD originate from the basic principles of Lean Construction, the vision to minimize waste, increase value, and continuous improvement. The application of Model-driven Software Engineering (MDSE) to BIM is a natural choice. Although several approaches utilizing MDSE for BIM have been proposed, so far no structured overview of the current state of the art has been conducted. Such an overview is vitally needed, because the existing literature is fragmented among multiple research areas. Consequently, in this paper, we present a systematic literature review on the application of MDSE to BIM, IPD and Lean Construction resulting in a systematically derived taxonomy, which we used to classify 97 papers published between 2008 and 2018. Based on the taxonomy, we provide an analysis of the classified research showing (a) where the discourse on model-driven construction engineering currently is, (b) the state of the art of model-driven techniques in construction engineering and (c) open research challenges
Hybrid multigrid methods for high-order discontinuous Galerkin discretizations
The present work develops hybrid multigrid methods for high-order
discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free
operator evaluation on tensor product elements is used to devise a
computationally efficient PDE solver. The multigrid hierarchy exploits all
possibilities of geometric, polynomial, and algebraic coarsening, targeting
engineering applications on complex geometries. Additionally, a transfer from
discontinuous to continuous function spaces is performed within the multigrid
hierarchy. This does not only further reduce the problem size of the
coarse-grid problem, but also leads to a discretization most suitable for
state-of-the-art algebraic multigrid methods applied as coarse-grid solver. The
relevant design choices regarding the selection of optimal multigrid coarsening
strategies among the various possibilities are discussed with the metric of
computational costs as the driving force for algorithmic selections. We find
that a transfer to a continuous function space at highest polynomial degree (or
on the finest mesh), followed by polynomial and geometric coarsening, shows the
best overall performance. The success of this particular multigrid strategy is
due to a significant reduction in iteration counts as compared to a transfer
from discontinuous to continuous function spaces at lowest polynomial degree
(or on the coarsest mesh). The coarsening strategy with transfer to a
continuous function space on the finest level leads to a multigrid algorithm
that is robust with respect to the penalty parameter of the SIPG method.
Detailed numerical investigations are conducted for a series of examples
ranging from academic test cases to more complex, practically relevant
geometries. Performance comparisons to state-of-the-art methods from the
literature demonstrate the versatility and computational efficiency of the
proposed multigrid algorithms
A Generalized Probabilistic Learning Approach for Multi-Fidelity Uncertainty Propagation in Complex Physical Simulations
Two of the most significant challenges in uncertainty propagation pertain to
the high computational cost for the simulation of complex physical models and
the high dimension of the random inputs. In applications of practical interest
both of these problems are encountered and standard methods for uncertainty
quantification either fail or are not feasible. To overcome the current
limitations, we propose a probabilistic multi-fidelity framework that can
exploit lower-fidelity model versions of the original problem in a small data
regime. The approach circumvents the curse of dimensionality by learning
dependencies between the outputs of high-fidelity models and lower-fidelity
models instead of explicitly accounting for the high-dimensional inputs. We
complement the information provided by a low-fidelity model with a
low-dimensional set of informative features of the stochastic input, which are
discovered by employing a combination of supervised and unsupervised
dimensionality reduction techniques. The goal of our analysis is an efficient
and accurate estimation of the full probabilistic response for a high-fidelity
model. Despite the incomplete and noisy information that low-fidelity
predictors provide, we demonstrate that accurate and certifiable estimates for
the quantities of interest can be obtained in the small data regime, i.e., with
significantly fewer high-fidelity model runs than state-of-the-art methods for
uncertainty propagation. We illustrate our approach by applying it to
challenging numerical examples such as Navier-Stokes flow simulations and
monolithic fluid-structure interaction problems.Comment: 31 pages, 14 figure
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