124 research outputs found
RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code
We have developed a new computer code, RAM, to solve the conservative
equations of special relativistic hydrodynamics (SRHD) using adaptive mesh
refinement (AMR) on parallel computers. We have implemented a
characteristic-wise, finite difference, weighted essentially non-oscillatory
(WENO) scheme using the full characteristic decomposition of the SRHD equations
to achieve fifth-order accuracy in space. For time integration we use the
method of lines with a third-order total variation diminishing (TVD)
Runge-Kutta scheme. We have also implemented fourth and fifth order Runge-Kutta
time integration schemes for comparison. The implementation of AMR and
parallelization is based on the FLASH code. RAM is modular and includes the
capability to easily swap hydrodynamics solvers, reconstruction methods and
physics modules. In addition to WENO we have implemented a finite volume module
with the piecewise parabolic method (PPM) for reconstruction and the modified
Marquina approximate Riemann solver to work with TVD Runge-Kutta time
integration. We examine the difficulty of accurately simulating shear flows in
numerical relativistic hydrodynamics codes. We show that under-resolved
simulations of simple test problems with transverse velocity components produce
incorrect results and demonstrate the ability of RAM to correctly solve these
problems. RAM has been tested in one, two and three dimensions and in
Cartesian, cylindrical and spherical coordinates. We have demonstrated
fifth-order accuracy for WENO in one and two dimensions and performed detailed
comparison with other schemes for which we show significantly lower convergence
rates. Extensive testing is presented demonstrating the ability of RAM to
address challenging open questions in relativistic astrophysics.Comment: ApJS in press, 21 pages including 18 figures (6 color figures
High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
We present a new family of very high order accurate direct
Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous
Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on
moving 2D Voronoi meshes that are regenerated at each time step and which
explicitly allow topology changes in time.
The Voronoi tessellations are obtained from a set of generator points that
move with the local fluid velocity. We employ an AREPO-type approach, which
rapidly rebuilds a new high quality mesh rearranging the element shapes and
neighbors in order to guarantee a robust mesh evolution even for vortex flows
and very long simulation times. The old and new Voronoi elements associated to
the same generator are connected to construct closed space--time control
volumes, whose bottom and top faces may be polygons with a different number of
sides. We also incorporate degenerate space--time sliver elements, needed to
fill the space--time holes that arise because of topology changes. The final
ALE FV-DG scheme is obtained by a redesign of the fully discrete direct ALE
schemes of Boscheri and Dumbser, extended here to moving Voronoi meshes and
space--time sliver elements. Our new numerical scheme is based on the
integration over arbitrary shaped closed space--time control volumes combined
with a fully-discrete space--time conservation formulation of the governing PDE
system. In this way the discrete solution is conservative and satisfies the GCL
by construction.
Numerical convergence studies as well as a large set of benchmarks for
hydrodynamics and magnetohydrodynamics (MHD) demonstrate the accuracy and
robustness of the proposed method. Our numerical results clearly show that the
new combination of very high order schemes with regenerated meshes with
topology changes lead to substantial improvements compared to direct ALE
methods on conforming meshes
Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement
Astrophysical relativistic flow problems require high resolution
three-dimensional numerical simulations. In this paper, we describe a new
parallel three-dimensional code for simulations of special relativistic
hydrodynamics (SRHD) using both spatially and temporally structured adaptive
mesh refinement (AMR). We used the method of lines to discretize the SRHD
equations spatially and a total variation diminishing (TVD) Runge-Kutta scheme
for time integration. For spatial reconstruction, we have implemented piecewise
linear method (PLM), piecewise parabolic method (PPM), third order convex
essentially non-oscillatory (CENO) and third and fifth order weighted
essentially non-oscillatory (WENO) schemes. Flux is computed using either
direct flux reconstruction or approximate Riemann solvers including HLL,
modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR
part of the code is built on top of the cosmological Eulerian AMR code {\sl
enzo}. We discuss the coupling of the AMR framework with the relativistic
solvers. Via various test problems, we emphasize the importance of resolution
studies in relativistic flow simulations because extremely high resolution is
required especially when shear flows are present in the problem. We also
present the results of two 3d simulations of astrophysical jets: AGN jets and
GRB jets. Resolution study of those two cases further highlights the need of
high resolutions to calculate accurately relativistic flow problems.Comment: 14 pages, 23 figures. A section on 3D GRB jet simulation added.
Accepted by ApJ
High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates
High-order reconstruction schemes for the solution of hyperbolic conservation
laws in orthogonal curvilinear coordinates are revised in the finite volume
approach. The formulation employs a piecewise polynomial approximation to the
zone-average values to reconstruct left and right interface states from within
a computational zone to arbitrary order of accuracy by inverting a
Vandermonde-like linear system of equations with spatially varying
coefficients. The approach is general and can be used on uniform and
non-uniform meshes although explicit expressions are derived for polynomials
from second to fifth degree in cylindrical and spherical geometries with
uniform grid spacing. It is shown that, in regions of large curvature, the
resulting expressions differ considerably from their Cartesian counterparts and
that the lack of such corrections can severely degrade the accuracy of the
solution close to the coordinate origin. Limiting techniques and monotonicity
constraints are revised for conventional reconstruction schemes, namely, the
piecewise linear method (PLM), third-order weighted essentially non-oscillatory
(WENO) scheme and the piecewise parabolic method (PPM).
The performance of the improved reconstruction schemes is investigated in a
number of selected numerical benchmarks involving the solution of both scalar
and systems of nonlinear equations (such as the equations of gas dynamics and
magnetohydrodynamics) in cylindrical and spherical geometries in one and two
dimensions. Results confirm that the proposed approach yields considerably
smaller errors, higher convergence rates and it avoid spurious numerical
effects at a symmetry axis.Comment: 37 pages, 12 Figures. Accepted for publication in Journal of
Compuational Physic
- …