25,034 research outputs found
Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws
A novel hybrid spectral difference/embedded finite volume method is
introduced in order to apply a discontinuous high-order method for large scale
engineering applications involving discontinuities in the flows with complex
geometries. In the proposed hybrid approach, the finite volume (FV) element,
consisting of structured FV subcells, is embedded in the base hexahedral
element containing discontinuity, and an FV based high-order shock-capturing
scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is
captured at the resolution of FV subcells within an embedded FV element. In the
smooth flow region, the SD element is used in the base hexahedral element.
Then, the governing equations are solved by the SD method. The SD method is
chosen for its low numerical dissipation and computational efficiency
preserving high-order accurate solutions. The coupling between the SD element
and the FV element is achieved by the globally conserved mortar method. In this
paper, the 5th-order WENO scheme with the characteristic decomposition is
employed as the shock-capturing scheme in the embedded FV element, and the
5th-order SD method is used in the smooth flow field.
The order of accuracy study and various 1D and 2D test cases are carried out,
which involve the discontinuities and vortex flows. Overall, it is shown that
the proposed hybrid method results in comparable or better simulation results
compared with the standalone WENO scheme when the same number of solution DOF
is considered in both SD and FV elements.Comment: 27 pages, 17 figures, 2 tables, Accepted for publication in the
Journal of Computational Physics, April 201
Spectral proper orthogonal decomposition
The identification of coherent structures from experimental or numerical data
is an essential task when conducting research in fluid dynamics. This typically
involves the construction of an empirical mode base that appropriately captures
the dominant flow structures. The most prominent candidates are the
energy-ranked proper orthogonal decomposition (POD) and the frequency ranked
Fourier decomposition and dynamic mode decomposition (DMD). However, these
methods fail when the relevant coherent structures occur at low energies or at
multiple frequencies, which is often the case. To overcome the deficit of these
"rigid" approaches, we propose a new method termed Spectral Proper Orthogonal
Decomposition (SPOD). It is based on classical POD and it can be applied to
spatially and temporally resolved data. The new method involves an additional
temporal constraint that enables a clear separation of phenomena that occur at
multiple frequencies and energies. SPOD allows for a continuous shifting from
the energetically optimal POD to the spectrally pure Fourier decomposition by
changing a single parameter. In this article, SPOD is motivated from
phenomenological considerations of the POD autocorrelation matrix and justified
from dynamical system theory. The new method is further applied to three sets
of PIV measurements of flows from very different engineering problems. We
consider the flow of a swirl-stabilized combustor, the wake of an airfoil with
a Gurney flap, and the flow field of the sweeping jet behind a fluidic
oscillator. For these examples, the commonly used methods fail to assign the
relevant coherent structures to single modes. The SPOD, however, achieves a
proper separation of spatially and temporally coherent structures, which are
either hidden in stochastic turbulent fluctuations or spread over a wide
frequency range
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
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication and computation resources.
Model-based robust design is difficult because of the complexity of the hybrid
dynamic models including continuous vehicle dynamics, the discrete models of
computations and communications, and the size of the problem. We will overview
recent advances in methodology and tools to model, analyze, and design robust
autonomous aerospace systems operating in uncertain environment, with stress on
efficient uncertainty quantification and robust design using the case studies
of the mission including model-based target tracking and search, and trajectory
planning in uncertain urban environment. To show that the methodology is
generally applicable to uncertain dynamical systems, we will also show examples
of application of the new methods to efficient uncertainty quantification of
energy usage in buildings, and stability assessment of interconnected power
networks
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