45,944 research outputs found
Critical phenomena and renormalization-group flow of multi-parameter \Phi^4 field theories
In the framework of the renormalization-group (RG) approach, critical
phenomena can be investigated by studying the RG flow of multi-parameter
field theories with an -component fundamental field, containing up
to 4th-order polynomials of the field. Some physically interesting systems
require field theories with several quadratic and quartic parameters,
depending essentially on their symmetry and symmetry-breaking pattern at the
transition. Results for their RG flow apply to disorder and/or frustrated
systems, anisotropic magnetic systems, density wave models, competing orderings
giving rise to multicritical behaviors. The general properties of the RG flow
in multi-parameter field theories are discussed. An overview of
field-theoretical results for some physically interesting cases is presented,
and compared with other theoretical approaches and experiments. Finally, this
RG approach is applied to investigate the nature of the finite-temperature
transition of QCD with light quarks.Comment: 22 pages, Plenary talk at the XXV International Symposium on Lattice
Field Theory, July 30 - August 4 2007, Regensburg, German
Time-domain harmonic balance method for aerodynamic and aeroelastic simulations of turbomachinery flows
A time-domain Harmonic Balance method is applied to simulate the blade row interactions and vibrations of state- of-the-art industrial turbomachinery configurations. The present harmonic balance approach is a time-integration scheme that turns a periodic or almost-periodic flow problem into the coupled resolution of several steady computations at different time samples of the period of interest. The coupling is performed by a spectral time-derivative operator that appears as a source term of all the steady problems. These are converged simultaneously making the method parallel in time. In this paper, a non-uniform time sampling is used to improve the robustness and accuracy regardless of the considered frequency set. Blade row interactions are studied within a 3.5-stage high-pressure axial compressor representative of the high-pressure core of modern turbofan engines. Comparisons with reference time-accurate computations show that four frequencies allow a fair match of the compressor performance, with a reduction of the computational time up to a factor 30. Finally, an aeroelastic study is performed for a counter-rotating fan stage, where the rear blade is submitted to a prescribed harmonic vibration along its first torsion mode. The aerodynamic damping is analysed, showing possible flutter
Towards High-order Methods for Rotorcraft Applications
This work presents CFD results obtained with an efficient, high-order, finite-volume scheme. The formulation is
based on the variable extrapolation MUSCL-scheme, and high-order spatial accuracy is achieved using correction
terms obtained through successive differentiation. The scheme is modified to cope with physical and multiblock
mesh interfaces, so stability, conservativeness, and high-order accuracy are guaranteed. Results with the proposed
scheme for steady flows, showed better wake and higher resolution of vortical structures compared with
the standard MUSCL, even when coarser meshes were employed. The method was also demonstrated for unsteady
flows using overset and moving grids for the UH-60A rotor in forward flight and the ERICA tiltrotor in aeroplane
mode. The present method adds CPU and memory overheads of 47% and 23%, respectively, in performing
multi-dimensional problems for routine computations
A matrix stability analysis of the carbuncle phenomenon
The carbuncle phenomenon is a shock instability mechanism which ruins all efforts to compute grid-aligned shock
waves using low-dissipative upwind schemes. The present study develops a stability analysis for two-dimensional steady shocks on structured meshes based on the matrix method. The numerical resolution of the corresponding eigenvalue problem confirms the typical odd–even form of the unstable mode and displays a Mach number threshold effect currently observed in computations. Furthermore, the present method indicates that the instability of steady shocks is not only governed by the upstream Mach number but also by the numerical shock structure. Finally, the source of the instability is localized in the upstream region, providing some clues to better understand and control the onset of the carbuncle
Velocity and energy relaxation in two-phase flows
In the present study we investigate analytically the process of velocity and
energy relaxation in two-phase flows. We begin our exposition by considering
the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This
model assumes each phase to possess its own velocity and energy variables.
Despite recent advances, the six equations model remains computationally
expensive for many practical applications. Moreover, its advection operator may
be non-hyperbolic which poses additional theoretical difficulties to construct
robust numerical schemes |Ghidaglia et al, 2001]. In order to simplify this
system, we complete momentum and energy conservation equations by relaxation
terms. When relaxation characteristic time tends to zero, velocities and
energies are constrained to tend to common values for both phases. As a result,
we obtain a simple two-phase model which was recently proposed for simulation
of violent aerated flows [Dias et al, 2010]. The preservation of invariant
regions and incompressible limit of the simplified model are also discussed.
Finally, several numerical results are presented.Comment: 37 pages, 10 figures. Other authors papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media
In this paper, we study upscaling for two-phase flows in strongly heterogeneous porous media. Upscaling a hyperbolic convection equation is known to be very difficult due to the presence of nonlocal memory effects. Even for a linear hyperbolic equation with a shear velocity field, the upscaled equation involves a nonlocal history dependent diffusion term, which is not amenable to computation. By performing a systematic multiscale analysis, we derive coupled equations for the average and the fluctuations for the two-phase flow. The homogenized equations for the coupled system are obtained by projecting the fluctuations onto a suitable subspace. This projection corresponds exactly to averaging along streamlines of the flow. Convergence of the multiscale analysis is verified numerically. Moreover, we show how to apply this multiscale analysis to upscale two-phase flows in practical applications
A multidimensional grid-adaptive relativistic magnetofluid code
A robust second order, shock-capturing numerical scheme for multi-dimensional
special relativistic magnetohydrodynamics on computational domains with
adaptive mesh refinement is presented. The base solver is a total variation
diminishing Lax-Friedrichs scheme in a finite volume setting and is combined
with a diffusive approach for controlling magnetic monopole errors. The
consistency between the primitive and conservative variables is ensured at all
limited reconstructions and the spatial part of the four velocity is used as a
primitive variable. Demonstrative relativistic examples are shown to validate
the implementation. We recover known exact solutions to relativistic MHD
Riemann problems, and simulate the shock-dominated long term evolution of
Lorentz factor 7 vortical flows distorting magnetic island chains.Comment: accepted for publication in Computer Physics Communication
Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows
In this work, we consider the discretization of nonlinear hyperbolic systems
in nonconservative form with the high-order discontinuous Galerkin spectral
element method (DGSEM) based on collocation of quadrature and interpolation
points (Kopriva and Gassner, J. Sci. Comput., 44 (2010), pp.136--155; Carpenter
et al., SIAM J. Sci. Comput., 36 (2014), pp.~B835-B867). We present a general
framework for the design of such schemes that satisfy a semi-discrete entropy
inequality for a given convex entropy function at any approximation order. The
framework is closely related to the one introduced for conservation laws by
Chen and Shu (J. Comput. Phys., 345 (2017), pp.~427--461) and relies on the
modification of the integral over discretization elements where we replace the
physical fluxes by entropy conservative numerical fluxes from Castro et al.
(SIAM J. Numer. Anal., 51 (2013), pp.~1371--1391), while entropy stable
numerical fluxes are used at element interfaces. Time discretization is
performed with strong-stability preserving Runge-Kutta schemes. We use this
framework for the discretization of two systems in one space-dimension: a
system with a nonconservative product associated to a
linearly-degenerate field for which the DGSEM fails to capture the physically
relevant solution, and the isentropic Baer-Nunziato model. For the latter, we
derive conditions on the numerical parameters of the discrete scheme to further
keep positivity of the partial densities and a maximum principle on the void
fractions. Numerical experiments support the conclusions of the present
analysis and highlight stability and robustness of the present schemes
Numerical Structure Analysis of Regular Hydrogen-Oxygen Detonations
Large-scale numerical simulations have been carried out to analyze the internal
wave structure of a regular oscillating low-pressure H2 : O2 : Ar-Chapman-Jouguet
detonation in two and three space-dimensions. The chemical reaction is modeled
with a non-equilibrium mechanism that consists of 34 elementary reactions and uses
nine thermally perfect gaseous species. A high local resolution is achieved dynamically
at run-time by employing a block-oriented adaptive finite volume method that
has been parallelized efficiently for massively parallel machines. Based on a highly
resolved two-dimensional simulation we analyze the temporal development of the
ow field around a triple point during a detonation cell in great detail. In particular,
the influence of the reinitiation phase at the beginning of a detonation cell
is discussed. Further on, a successful simulation of the cellular structure in three
space-dimensions for the same configuration is presented. The calculation reproduces
the experimentally observed three-dimensional mode of propagation called
"rectangular-mode-in-phase" with zero phase shift between the transverse waves in
both space-directions perpendicular to the detonation front and shows the same
oscillation period as the two-dimensional case
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