26,191 research outputs found
Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations
We introduce a \textit{non-modal} analysis technique that characterizes the
diffusion properties of spectral element methods for linear
convection-diffusion systems. While strictly speaking only valid for linear
problems, the analysis is devised so that it can give critical insights on two
questions: (i) Why do spectral element methods suffer from stability issues in
under-resolved computations of nonlinear problems? And, (ii) why do they
successfully predict under-resolved turbulent flows even without a
subgrid-scale model? The answer to these two questions can in turn provide
crucial guidelines to construct more robust and accurate schemes for complex
under-resolved flows, commonly found in industrial applications. For
illustration purposes, this analysis technique is applied to the hybridized
discontinuous Galerkin methods as representatives of spectral element methods.
The effect of the polynomial order, the upwinding parameter and the P\'eclet
number on the so-called \textit{short-term diffusion} of the scheme are
investigated. From a purely non-modal analysis point of view, polynomial orders
between and with standard upwinding are well suited for under-resolved
turbulence simulations. For lower polynomial orders, diffusion is introduced in
scales that are much larger than the grid resolution. For higher polynomial
orders, as well as for strong under/over-upwinding, robustness issues can be
expected. The non-modal analysis results are then tested against under-resolved
turbulence simulations of the Burgers, Euler and Navier-Stokes equations. While
devised in the linear setting, our non-modal analysis succeeds to predict the
behavior of the scheme in the nonlinear problems considered
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis
of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD
equations as they are particularly useful for mathematically modeling a wide
variety of magnetized fluids. In order to be self-contained we first motivate
the physical properties of a magnetic fluid and how it should behave under the
laws of thermodynamics. Next, we introduce a mathematical model built from
hyperbolic partial differential equations (PDEs) that translate physical laws
into mathematical equations. After an overview of the continuous analysis, we
thoroughly describe the derivation of a numerical approximation of the ideal
MHD system that remains consistent to the continuous thermodynamic principles.
The derivation of the method and the theorems contained within serve as the
bulk of the review article. We demonstrate that the derived numerical
approximation retains the correct entropic properties of the continuous model
and show its applicability to a variety of standard numerical test cases for
MHD schemes. We close with our conclusions and a brief discussion on future
work in the area of entropy consistent numerical methods and the modeling of
plasmas
Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations
In melt-blowing very thin liquid fiber jets are spun due to high-velocity air
streams. In literature there is a clear, unsolved discrepancy between the
measured and computed jet attenuation. In this paper we will verify numerically
that the turbulent velocity fluctuations causing a random aerodynamic drag on
the fiber jets -- that has been neglected so far -- are the crucial effect to
close this gap. For this purpose, we model the velocity fluctuations as vector
Gaussian random fields on top of a k-epsilon turbulence description and develop
an efficient sampling procedure. Taking advantage of the special covariance
structure the effort of the sampling is linear in the discretization and makes
the realization possible
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
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
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