252 research outputs found
SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics
We introduce a new relativistic astrophysics code, SpECTRE, that combines a
discontinuous Galerkin method with a task-based parallelism model. SpECTRE's
goal is to achieve more accurate solutions for challenging relativistic
astrophysics problems such as core-collapse supernovae and binary neutron star
mergers. The robustness of the discontinuous Galerkin method allows for the use
of high-resolution shock capturing methods in regions where (relativistic)
shocks are found, while exploiting high-order accuracy in smooth regions. A
task-based parallelism model allows efficient use of the largest supercomputers
for problems with a heterogeneous workload over disparate spatial and temporal
scales. We argue that the locality and algorithmic structure of discontinuous
Galerkin methods will exhibit good scalability within a task-based parallelism
framework. We demonstrate the code on a wide variety of challenging benchmark
problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the
code's scalability including its strong scaling on the NCSA Blue Waters
supercomputer up to the machine's full capacity of 22,380 nodes using 671,400
threads.Comment: 41 pages, 13 figures, and 7 tables. Ancillary data contains
simulation input file
High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
The paper develops high-order accurate physical-constraints-preserving finite
difference WENO schemes for special relativistic hydrodynamical (RHD)
equations, built on the local Lax-Friedrich splitting, the WENO reconstruction,
the physical-constraints-preserving flux limiter, and the high-order strong
stability preserving time discretization. They are extensions of the
positivity-preserving finite difference WENO schemes for the non-relativistic
Euler equations. However, developing physical-constraints-preserving methods
for the RHD system becomes much more difficult than the non-relativistic case
because of the strongly coupling between the RHD equations, no explicit
expressions of the primitive variables and the flux vectors, in terms of the
conservative vector, and one more physical constraint for the fluid velocity in
addition to the positivity of the rest-mass density and the pressure. The key
is to prove the convexity and other properties of the admissible state set and
discover a concave function with respect to the conservative vector replacing
the pressure which is an important ingredient to enforce the
positivity-preserving property for the non-relativistic case. Several one- and
two-dimensional numerical examples are used to demonstrate accuracy,
robustness, and effectiveness of the proposed physical-constraints-preserving
schemes in solving RHD problems with large Lorentz factor, or strong
discontinuities, or low rest-mass density or pressure etc.Comment: 39 pages, 13 figure
A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
A well-balanced discontinuous Galerkin method for the first--order Z4 formulation of the Einstein--Euler system
In this paper we develop a new well-balanced discontinuous Galerkin (DG)
finite element scheme with subcell finite volume (FV) limiter for the numerical
solution of the Einstein--Euler equations of general relativity based on a
first order hyperbolic reformulation of the Z4 formalism. The first order Z4
system, which is composed of 59 equations, is analyzed and proven to be
strongly hyperbolic for a general metric. The well-balancing is achieved for
arbitrary but a priori known equilibria by subtracting a discrete version of
the equilibrium solution from the discretized time-dependent PDE system.
Special care has also been taken in the design of the numerical viscosity so
that the well-balancing property is achieved. As for the treatment of low
density matter, e.g. when simulating massive compact objects like neutron stars
surrounded by vacuum, we have introduced a new filter in the conversion from
the conserved to the primitive variables, preventing superluminal velocities
when the density drops below a certain threshold, and being potentially also
very useful for the numerical investigation of highly rarefied relativistic
astrophysical flows. Thanks to these improvements, all standard tests of
numerical relativity are successfully reproduced, reaching three achievements:
(i) we are able to obtain stable long term simulations of stationary black
holes, including Kerr black holes with extreme spin, which after an initial
perturbation return perfectly back to the equilibrium solution up to machine
precision; (ii) a (standard) TOV star under perturbation is evolved in pure
vacuum () up to with no need to introduce any artificial
atmosphere around the star; and, (iii) we solve the head on collision of two
punctures black holes, that was previously considered un--tractable within the
Z4 formalism.Comment: 44 pages, 15 figure
Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting)
This small collaborative workshop brought together
experts from the Sino-German project working in the field of advanced numerical methods for
hyperbolic balance laws. These are particularly important for compressible fluid flows and related systems of equations. The investigated numerical methods were finite volume/finite difference, discontinuous Galerkin methods, and kinetic-type schemes. We have discussed challenging open mathematical research problems in this field, such as multidimensional shock waves, interfaces with different phases or efficient and problem suited adaptive algorithms. Consequently, our main objective was to discuss novel high-order accurate schemes that reliably approximate underlying physical models and preserve important physically relevant properties. Theoretical questions concerning the
convergence of numerical methods and proper solution concepts were addressed as well
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
We present the first high order one-step ADER-WENO finite volume scheme with
Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial
accuracy is obtained through a WENO reconstruction, while a high order one-step
time discretization is achieved using a local space-time discontinuous Galerkin
predictor method. Due to the one-step nature of the underlying scheme, the
resulting algorithm is particularly well suited for an AMR strategy on
space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR
property has been implemented 'cell-by-cell', with a standard tree-type
algorithm, while the scheme has been parallelized via the Message Passing
Interface (MPI) paradigm. The new scheme has been tested over a wide range of
examples for nonlinear systems of hyperbolic conservation laws, including the
classical Euler equations of compressible gas dynamics and the equations of
magnetohydrodynamics (MHD). High order in space and time have been confirmed
via a numerical convergence study and a detailed analysis of the computational
speed-up with respect to highly refined uniform meshes is also presented. We
also show test problems where the presented high order AMR scheme behaves
clearly better than traditional second order AMR methods. The proposed scheme
that combines for the first time high order ADER methods with space--time
adaptive grids in two and three space dimensions is likely to become a useful
tool in several fields of computational physics, applied mathematics and
mechanics.Comment: With updated bibliography informatio
THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics
We present THC: a new high-order flux-vector-splitting code for Newtonian and
special-relativistic hydrodynamics designed for direct numerical simulations of
turbulent flows. Our code implements a variety of different reconstruction
algorithms, such as the popular weighted essentially non oscillatory and
monotonicity-preserving schemes, or the more specialised bandwidth-optimised
WENO scheme that has been specifically designed for the study of compressible
turbulence. We show the first systematic comparison of these schemes in
Newtonian physics as well as for special-relativistic flows. In particular we
will present the results obtained in simulations of grid-aligned and oblique
shock waves and nonlinear, large-amplitude, smooth adiabatic waves. We will
also discuss the results obtained in classical benchmarks such as the
double-Mach shock reflection test in Newtonian physics or the linear and
nonlinear development of the relativistic Kelvin-Helmholtz instability in two
and three dimensions. Finally, we study the turbulent flow induced by the
Kelvin-Helmholtz instability and we show that our code is able to obtain
well-converged velocity spectra, from which we benchmark the effective
resolution of the different schemes.Comment: Updated to match the published versio
The Inertial Range of Turbulence in the Inner Heliosheath and in the Local Interstellar Medium
The governing mechanisms of magnetic field annihilation in the outer heliosphere is an intriguing topic. It is currently believed that the turbulent fluctuations pervade the inner heliosheath (IHS) and the Local Interstellar Medium (LISM). Turbulence, magnetic reconnection, or their reciprocal link may be responsible for magnetic energy conversion in the IHS.
As 1-day averaged data are typically used, the present literature mainly concerns large-scale analysis and does not describe inertial-cascade dynamics of turbulence in the IHS. Moreover, lack of spectral analysis make IHS dynamics remain critically understudied. Our group showed that 48-s MAG data from the Voyager mission are appropriate for a power spectral analysis over a frequency range of five decades, from 5e-8 Hz to 1e-2 Hz [Gallana et al., JGR 121 (2016)]. Special spectral estimation techniques are used to deal with the large amount of missing data (70%). We provide the first clear evidence of an inertial-cascade range of turbulence (spectral index is between -2 and -1.5). A spectral break at about 1e-5 Hz is found to separate the inertial range from the enegy-injection range (1/f energy decay). Instrumental noise bounds our investigation to frequencies lower than 5e-4 Hz. By considering several consecutive periods after 2009 at both V1 and V2, we show that the extension and the spectral energy decay of these two regimes may be indicators of IHS regions governed by different physical processes. We describe fluctuations’ regimes in terms of spectral energy density, anisotropy, compressibility, and statistical analysis of intermittency.
In the LISM, it was theorized that pristine interstellar turbulence may coexist with waves from the IHS, however this is still a debated topic. We observe that the fluctuating magnetic energy cascades as a power law with spectral index in the range [-1.35, -1.65] in the whole range of frequencies unaffected by noise. No spectral break is observed, nor decaying turbulence
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