2,559 research outputs found
A three-dimensional multidimensional gas-kinetic scheme for the Navier-Stokes equations under gravitational fields
This paper extends the gas-kinetic scheme for one-dimensional inviscid
shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to
multidimensional gas dynamic equations under gravitational fields. Four
important issues in the construction of a well-balanced scheme for gas dynamic
equations are addressed. First, the inclusion of the gravitational source term
into the flux function is necessary. Second, to achieve second-order accuracy
of a well-balanced scheme, the Chapman-Enskog expansion of the Boltzmann
equation with the inclusion of the external force term is used. Third, to avoid
artificial heating in an isolated system under a gravitational field, the
source term treatment inside each cell has to be evaluated consistently with
the flux evaluation at the cell interface. Fourth, the multidimensional
approach with the inclusion of tangential gradients in two-dimensional and
three-dimensional cases becomes important in order to maintain the accuracy of
the scheme. Many numerical examples are used to validate the above issues,
which include the comparison between the solutions from the current scheme and
the Strang splitting method. The methodology developed in this paper can also
be applied to other systems, such as semi-conductor device simulations under
electric fields.Comment: The name of first author was misspelled as C.T.Tian in the published
paper. 35 pages,9 figure
An improved SPH scheme for cosmological simulations
We present an implementation of smoothed particle hydrodynamics (SPH) with
improved accuracy for simulations of galaxies and the large-scale structure. In
particular, we combine, implement, modify and test a vast majority of SPH
improvement techniques in the latest instalment of the GADGET code. We use the
Wendland kernel functions, a particle wake-up time-step limiting mechanism and
a time-dependent scheme for artificial viscosity, which includes a high-order
gradient computation and shear flow limiter. Additionally, we include a novel
prescription for time-dependent artificial conduction, which corrects for
gravitationally induced pressure gradients and largely improves the SPH
performance in capturing the development of gas-dynamical instabilities. We
extensively test our new implementation in a wide range of hydrodynamical
standard tests including weak and strong shocks as well as shear flows,
turbulent spectra, gas mixing, hydrostatic equilibria and self-gravitating gas
clouds. We jointly employ all modifications; however, when necessary we study
the performance of individual code modules. We approximate hydrodynamical
states more accurately and with significantly less noise than standard SPH.
Furthermore, the new implementation promotes the mixing of entropy between
different fluid phases, also within cosmological simulations. Finally, we study
the performance of the hydrodynamical solver in the context of radiative galaxy
formation and non-radiative galaxy cluster formation. We find galactic disks to
be colder, thinner and more extended and our results on galaxy clusters show
entropy cores instead of steadily declining entropy profiles. In summary, we
demonstrate that our improved SPH implementation overcomes most of the
undesirable limitations of standard SPH, thus becoming the core of an efficient
code for large cosmological simulations.Comment: 21 figures, 2 tables, accepted to MNRA
Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows
The present paper addresses the development and implementation of the first
high-order Flux Reconstruction (FR) solver for high-speed flows within the
open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid
Dynamics) platform. The resulting solver is fully implicit and able to simulate
compressible flow problems governed by either the Euler or the Navier-Stokes
equations in two and three dimensions. Furthermore, it can run in parallel on
multiple CPU-cores and is designed to handle unstructured grids consisting of
both straight and curved edged quadrilateral or hexahedral elements. While most
of the implementation relies on state-of-the-art FR algorithms, an improved and
more case-independent shock capturing scheme has been developed in order to
tackle the first viscous hypersonic simulations using the FR method. Extensive
verification of the FR solver has been performed through the use of
reproducible benchmark test cases with flow speeds ranging from subsonic to
hypersonic, up to Mach 17.6. The obtained results have been favorably compared
to those available in literature. Furthermore, so-called super-accuracy is
retrieved for certain cases when solving the Euler equations. The strengths of
the FR solver in terms of computational accuracy per degree of freedom are also
illustrated. Finally, the influence of the characterizing parameters of the FR
method as well as the the influence of the novel shock capturing scheme on the
accuracy of the developed solver is discussed
Supercomputer implementation of finite element algorithms for high speed compressible flows
Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes
Ignition of Deflagration and Detonation Ahead of the Flame due to Radiative Preheating of Suspended Micro Particles
We study a flame propagating in the gaseous combustible mixture with
suspended inert particles. The gas is assumed to be transparent for the
radiation emitted by the combustion products, while particles absorb and
re-emit the radiation. Thermal radiation heats the particles, which in turn
transfer the heat to the surrounding gaseous mixture by means of heat
conduction, so that the gas temperature lags that of the particles. We consider
different scenarios depending on the spatial distribution of the particles,
their size and the number density. In the case of uniform distribution of the
particles the radiation causes a modest increase of the temperature ahead of
the flame and the corresponding increase of the flame velocity. The effects of
radiation preheating is stronger for a flame with smaller normal velocity. In
the case of non-uniform distribution of the particles, such that the particles
number density is smaller just ahead of the flame and increases in the distant
region ahead of the flame, the preheating caused by the thermal radiation may
trigger additional independent source of ignition. This scenario requires the
formation of a temperature gradient with the maximum temperature sufficient for
ignition in the region of denser particles cloud ahead of the advancing flame.
Depending on the steepness of the temperature gradient formed in the unburned
mixture, either deflagration or detonation can be initiated via the Zeldovich's
gradient mechanism. The ignition and the resulting combustion regimes depend on
the temperature profile which is formed in effect of radiation absorption and
gas-dynamic expansion. In the case of coal dust flames propagating through a
layered dust cloud the effect of radiation heat transfer can result in the
propagation of combustion wave with velocity up to 1000m/s and can be a
plausible explanation of the origin of dust explosion in coal mines.Comment: 45 pages, 14 figures. Accepted for publication Combustion and Flame
29 June 201
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