27 research outputs found
Towards a unified lattice kinetic scheme for relativistic hydrodynamics
We present a systematic derivation of relativistic lattice kinetic equations
for finite-mass particles, reaching close to the zero-mass ultra-relativistic
regime treated in the previous literature. Starting from an expansion of the
Maxwell-Juettner distribution on orthogonal polynomials, we perform a
Gauss-type quadrature procedure and discretize the relativistic Boltzmann
equation on space-filling Cartesian lattices. The model is validated through
numerical comparison with standard benchmark tests and solvers in relativistic
fluid dynamics such as Boltzmann approach multiparton scattering (BAMPS) and
previous relativistic lattice Boltzmann models. This work provides a
significant step towards the formulation of a unified relativistic lattice
kinetic scheme, covering both massive and near-massless particles regimes
Kinetic approach to relativistic dissipation
Despite a long record of intense efforts, the basic mechanisms by which
dissipation emerges from the microscopic dynamics of a relativistic fluid still
elude a complete understanding. In particular, no unique pathway from kinetic
theory to hydrodynamics has been identified as yet, with different approaches
leading to different values of the transport coefficients. In this Letter, we
approach the problem by matching data from lattice kinetic simulations with
analytical predictions. Our numerical results provide neat evidence in favour
of the Chapman-Enskog procedure, as suggested by recently theoretical analyses,
along with qualitative hints at the basic reasons why the Chapman-Enskog
expansion might be better suited than Grad's method to capture the emergence of
dissipative effects in relativistic fluids
Energy-efficiency evaluation of Intel KNL for HPC workloads
Energy consumption is increasingly becoming a limiting factor to the design
of faster large-scale parallel systems, and development of energy-efficient and
energy-aware applications is today a relevant issue for HPC code-developer
communities. In this work we focus on energy performance of the Knights Landing
(KNL) Xeon Phi, the latest many-core architecture processor introduced by Intel
into the HPC market. We take into account the 64-core Xeon Phi 7230, and
analyze its energy performance using both the on-chip MCDRAM and the regular
DDR4 system memory as main storage for the application data-domain. As a
benchmark application we use a Lattice Boltzmann code heavily optimized for
this architecture and implemented using different memory data layouts to store
its lattice. We assessthen the energy consumption using different memory
data-layouts, kind of memory (DDR4 or MCDRAM) and number of threads per core
Probing bulk viscosity in relativistic flows
We derive an analytical connection between kinetic relaxation rate and bulk
viscosity of a relativistic fluid in d spatial dimensions, all the way from the
ultra-relativistic down to the near non-relativistic regime. Our derivation is
based on both Chapman-Enskog asymptotic expansion and Grad's method of moments.
We validate our theoretical results against a benchmark flow, providing further
evidence of the correctness of the Chapman-Enskog approach; we define the range
of validity of this approach and provide evidence of mounting departures at
increasing Knudsen number. Finally, we present numerical simulations of
transport processes in quark gluon plasmas, with special focus on the effects
of bulk viscosity which might prove amenable to future experimental
verification
Relativistic dissipation obeys Chapman-Enskog asymptotics: analytical and numerical evidence as a basis for accurate kinetic simulations
We present an analytical derivation of the transport coefficients of a
relativistic gas in (2+1) dimensions for both Chapman-Enskog (CE) asymptotics
and Grad's expansion methods. Moreover, we develop a systematic calibration
method, connecting the relaxation time of relativistic kinetic theory to the
transport parameters of the associated dissipative hydrodynamic equations.
Comparison between the analytical results and numerical simulations, shows that
the CE method correctly captures dissipative effects, while Grad's method does
not. The resulting calibration procedure based on the CE method opens the way
to the quantitative kinetic description of dissipative relativistic fluid
dynamics under fairly general conditions, namely flows with strongly
non-linearities, in non-ideal geometries, across both ultra-relativistic and
near-non-relativistic regimes
Numerical evidence of electron hydrodynamic whirlpools in graphene samples
We present an extension of recent relativistic Lattice Boltzmann methods
based on Gaussian quadratures for the study of fluids in (2+1) dimensions. The
new method is applied to the analysis of electron flow in graphene samples
subject to electrostatic drive; we show that the flow displays hydro-electronic
whirlpools in accordance with recent analytical calculations as well as
experimental results
A Lattice Boltzmann Method for relativistic rarefied flows in (2+1) dimensions
We propose an extension to recently developed Relativistic Lattice Boltzmann solvers (RLBM), which allows the simulation of flows close to the free streaming limit. Following previous works Ambruş and Blaga (2018), we use product quadrature rules and select weights and nodes by separately discretizing the radial and the angular components. This procedure facilitates the development of quadrature-based RLBM with increased isotropy levels, thus improving the accuracy of the method for the simulation of flows beyond the hydrodynamic regime. In order to quantify the improvement of this discretization procedure over existing methods, we perform numerical tests of shock waves in one and two spatial dimensions in various kinetic regimes across the hydrodynamic and the free-streaming limits.</p
Prospects for the detection of electronic pre-turbulence in graphene
Based on extensive numerical simulations, accounting for electrostatic
interactions and dissipative electron-phonon scattering, we propose
experimentally realizable geometries capable of sustaining electronic
pre-turbulence in graphene samples. In particular, pre-turbulence is predicted
to occur at experimentally attainable values of the Reynolds number between 10
and 50, over a broad spectrum of frequencies between 10 and 100 GHz
Beyond moments: relativistic Lattice-Boltzmann methods for radiative transport in computational astrophysics
We present a new method for the numerical solution of the radiative-transfer
equation (RTE) in multidimensional scenarios commonly encountered in
computational astrophysics. The method is based on the direct solution of the
Boltzmann equation via an extension of the Lattice Boltzmann (LB) equation and
allows to model the evolution of the radiation field as it interacts with a
background fluid, via absorption, emission, and scattering. As a first
application of this method, we restrict our attention to a frequency
independent ("grey") formulation within a special-relativistic framework, which
can be employed also for classical computational astrophysics. For a number of
standard tests that consider the performance of the method in optically thin,
optically thick and intermediate regimes with a static fluid, we show the
ability of the LB method to produce accurate and convergent results matching
the analytic solutions. We also contrast the LB method with commonly employed
moment-based schemes for the solution of the RTE, such as the M1 scheme. In
this way, we are able to highlight that the LB method provides the correct
solution for both non-trivial free-streaming scenarios and the intermediate
optical-depth regime, for which the M1 method either fails or provides
inaccurate solutions. When coupling to a dynamical fluid, on the other hand, we
present the first self-consistent solution of the RTE with LB methods within a
relativistic-hydrodynamic scenario. Finally, we show that besides providing
more accurate results in all regimes, the LB method features smaller or
comparable computational costs compared to the M1 scheme.Comment: 22 pages, 16 figures, matches version accepted in MNRA