1,980 research outputs found
Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows
The aim of the present paper is to provide a comparison between several
finite-volume methods of different numerical accuracy: second-order Godunov
method with PPM interpolation and high-order finite-volume WENO method. The
results show that while on a smooth problem the high-order method perform
better than the second-order one, when the solution contains a shock all the
methods collapse to first-order accuracy. In the context of the decay of
compressible homogeneous isotropic turbulence with shocklets, the actual
overall order of accuracy of the methods reduces to second-order, despite the
use of fifth-order reconstruction schemes at cell interfaces. Most important,
results in terms of turbulent spectra are similar regardless of the numerical
methods employed, except that the PPM method fails to provide an accurate
representation in the high-frequency range of the spectra. It is found that
this specific issue comes from the slope-limiting procedure and a novel hybrid
PPM/WENO method is developed that has the ability to capture the turbulent
spectra with the accuracy of a high-order method, but at the cost of the
second-order Godunov method. Overall, it is shown that virtually the same
physical solution can be obtained much faster by refining a simulation with the
second-order method and carefully chosen numerical procedures, rather than
running a coarse high-order simulation. Our results demonstrate the importance
of evaluating the accuracy of a numerical method in terms of its actual
spectral dissipation and dispersion properties on mixed smooth/shock cases,
rather than by the theoretical formal order of convergence rate.Comment: This paper was previously composed of 2 parts, and this submission
was part 1. It is now replaced by the combined pape
Stable, entropy-consistent, and localized artificial-diffusivity method for capturing discontinuities
In this work, a localized artificial-viscosity/diffusivity method is proposed
for accurately capturing discontinuities in compressible flows. There have been
numerous efforts to improve the artificial diffusivity formulation in the last
two decades, through appropriate localization of the artificial bulk viscosity
for capturing shocks. However, for capturing contact discontinuities, either a
density or internal energy variable is used as a detector. An issue with this
sensor is that it not only detects contact discontinuities, but also falsely
detects the regions of shocks and vortical motions. Using this detector to add
artificial mass/thermal diffusivity for capturing contact discontinuities is
hence unnecessarily dissipative. To overcome this issue, we propose a sensor
similar to the Ducros sensor (for shocks) to detect contact discontinuities,
and further localize artificial mass/thermal diffusivity for capturing contact
discontinuities.
The proposed method contains coefficients that are less sensitive to the
choice of the flow problem. This is achieved by improved localization of the
artificial diffusivity in the present method. A discretely consistent
dissipative flux formulation is presented and is coupled with a robust
low-dissipative scheme, which eliminates the need for filtering the solution
variables. The proposed method also does not require filtering for the
discontinuity detector/sensor functions, which is typically done to smear out
the artificial fluid properties and obtain stable solutions. Hence, the
challenges associated with extending the filtering procedure for unstructured
grids is eliminated, thereby, making the proposed method easily applicable for
unstructured grids. Finally, a straightforward extension of the proposed method
to two-phase flows is also presented.Comment: 24 pages, 11 figures, Under review in the Physical Review Fluids
journa
Comparison of Subgrid-scale Viscosity Models and Selective Filtering Strategy for Large-eddy Simulations
Explicitly filtered large-eddy simulations (LES), combining high-accuracy schemes with the use of a selective filtering without adding an explicit subgrid-scales (SGS) model, are carried out for the Taylor-Green-vortex and the supersonic-boundary-layer cases. First, the present approach is validated against direct numerical simulation (DNS) results. Subsequently, several SGS models are implemented in order to investigate if they can improve the initial filter-based methodology. It is shown that the most accurate results are obtained when the filtering is used alone as an implicit model, and for a minimal cost. Moreover, the tests for the Taylor-Green vortex indicate that the discretization error from the numerical methods, notably the dissipation error from the high-order filtering, can have a greater influence than the SGS models
Assessment of a high-order shock-capturing central-difference scheme for hypersonic turbulent flow simulations
High-speed turbulent flows are encountered in most space-related applications
(including exploration, tourism and defense fields) and represent a subject of
growing interest in the last decades. A major challenge in performing
high-fidelity simulations of such flows resides in the stringent requirements
for the numerical schemes to be used. These must be robust enough to handle
strong, unsteady discontinuities, while ensuring low amounts of intrinsic
dissipation in smooth flow regions. Furthermore, the wide range of temporal and
spatial active scales leads to concurrent needs for numerical stabilization and
accurate representation of the smallest resolved flow scales in cases of
under-resolved configurations. In this paper, we present a finite-difference
high-order shock-capturing technique based on Jameson's artificial diffusivity
methodology. The resulting scheme is ninth-order-accurate far from
discontinuities and relies on the addition of artificial dissipation close to
large gradients. The shock detector is slightly revised to enhance its
selectivity and avoid spurious activations of the shock-capturing term. A suite
of test cases ranging from 1D to 3D configurations (namely, shock tubes,
Shu-Osher problem, isentropic vortex advection, under-expanded jet,
compressible Taylor-Green Vortex, supersonic and hypersonic turbulent boundary
layers) is analysed in order to test the capability of the proposed numerical
strategy to handle a large variety of problems, ranging from
calorically-perfect air to multi-species reactive flows. Results obtained on
under-resolved grids are also considered to test the applicability of the
proposed strategy in the context of implicit Large-Eddy Simulations
Implicit large eddy simulation for unsteady multi-component compressible turbulent flows
Numerical methods for the simulation of shock-induced turbulent mixing have been
investigated, focussing on Implicit Large Eddy Simulation. Shock-induced turbulent
mixing is of particular importance for many astrophysical phenomena, inertial confinement
fusion, and mixing in supersonic combustion. These disciplines are particularly
reliant on numerical simulation, as the extreme nature of the flow in question makes
gathering accurate experimental data difficult or impossible.
A detailed quantitative study of homogeneous decaying turbulence demonstrates that
existing state of the art methods represent the growth of turbulent structures and the decay
of turbulent kinetic energy to a reasonable degree of accuracy. However, a key observation
is that the numerical methods are too dissipative at high wavenumbers (short
wavelengths relative to the grid spacing). A theoretical analysis of the dissipation of
kinetic energy in low Mach number flows shows that the leading order dissipation rate
for Godunov-type schemes is proportional to the speed of sound and the velocity jump
across the cell interface squared. This shows that the dissipation of Godunov-type
schemes becomes large for low Mach flow features, hence impeding the development
of fluid instabilities, and causing overly dissipative turbulent kinetic energy spectra.
It is shown that this leading order term can be removed by locally modifying the reconstruction
of the velocity components. As the modification is local, it allows the
accurate simulation of mixed compressible/incompressible flows without changing the
formulation of the governing equations. In principle, the modification is applicable to
any finite volume compressible method which includes a reconstruction stage. Extensive
numerical tests show great improvements in performance at low Mach compared
to the standard scheme, significantly improving turbulent kinetic energy spectra, and
giving the correct Mach squared scaling of pressure and density variations down to
Mach 10−4. The proposed modification does not significantly affect the shock capturing
ability of the numerical scheme.
The modified numerical method is validated through simulations of compressible,
deep, open cavity flow where excellent results are gained with minimal modelling
effort. Simulations of single and multimode Richtmyer-Meshkov instability show that
the modification gives equivalent results to the standard scheme at twice the grid resolution
in each direction. This is equivalent to sixteen times decrease in computational
time for a given quality of results. Finally, simulations of a shock-induced turbulent
mixing experiment show excellent qualitative agreement with available experimental
data
A low-numerical dissipation, patch-based adaptive-mesh-refinement method for large-eddy simulation of compressible flows
This paper describes a hybrid finite-difference method for the large-eddy simulation of compressible flows with low-numerical dissipation and structured adaptive mesh refinement (SAMR). A conservative flux-based approach is described with an explicit centered scheme used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. Three-dimensional numerical simulations of a Richtmyer-Meshkov instability are presented
Study of compressible turbulent flows in supersonic environment by large-eddy simulation
A Large-Eddy Simulation (LES) methodology adapted to the resolution of high Reynolds number turbulent flows in supersonic conditions was proposed and developed. A novel numerical scheme was designed, that switches from a low-dissipation
central scheme for turbulence resolution to a flux difference splitting scheme in regions
of discontinuities. Furthermore, a state-of-the-art closure model was extended in order
to take compressibility effects and the action of shock / turbulence interaction into account.
The proposed method was validated against fundamental studies of high speed flows and shock / turbulence interaction studies. This new LES approach was employed for the study of shock / turbulent shear layer interaction as a mixing-augmentation technique, and highlighted the efficiency in mixing improvement after the interaction, but also the limited spatial extent of this turbulent enhancement. A second practical
study was conducted by simulating the injection of a sonic jet normally to a supersonic crossflow. The validity of the simulation was assessed by comparison with experimental
data, and the dynamics of the interaction was examined. The sources of vortical structures were identified, with a particular emphasis on the impact of the
flow speed onto the vortical evolution.Ph.D.Committee Chair: Menon, Suresh; Committee Member: Ruffin, Stephen; Committee Member: Sankar, Lakshmi; Committee Member: Seitzman, Jerry; Committee Member: Stoesser, Thorste
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