1,192 research outputs found
Two-Dimensional Central-Upwind Schemes for Curvilinear Grids and Application to Gas Dynamics with Angular Momentum
In this work we present new second order semi-discrete central schemes for
systems of hyperbolic conservation laws on curvilinear grids. Our methods
generalise the two-dimensional central-upwind schemes developed by Kurganov and
Tadmor. In these schemes we account for area and volume changes in the
numerical flux functions due to the non-cartesian geometries. In case of
vectorial conservation laws we introduce a general prescription of the
geometrical source terms valid for various orthogonal curvilinear coordinate
systems. The methods are applied to the two-dimensional Euler equations of
inviscid gas dynamics with and without angular momentum transport. In the
latter case we introduce a new test problem to examine the detailed
conservation of specific angular momentum.Comment: 38 pages, 1
ITER is a challenge of global society
Nowadays, humanity requires more and more and more energy. What is more, present sources of energy can‘t provide modern society with it, besides, they are not rational and ecological enough, so that tends to be the only way to create new, radically new, source of energy and it is fusion reactor. Fusion reactor is a source of energy of new generation. ITER (International Thermonuclear Experimental Reactor) is a first step to create a commercially viable reactor
Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms
We present numerical relativity simulations of nine-orbit equal-mass binary
neutron star covering the quasicircular late inspiral and merger. The extracted
gravitational waveforms are analyzed for convergence and accuracy. Second order
convergence is observed up to contact, i.e. about 3-4 cycles to merger; error
estimates can be made up to this point. The uncertainties on the phase and the
amplitude are dominated by truncation errors and can be minimized to 0.13 rad
and less then 1%, respectively, by using several simulations and extrapolating
in resolution. In the latter case finite-radius extraction uncertainties become
a source of error of the same order and have to be taken into account. The
waveforms are tested against accuracy standards for data analysis. The
uncertainties on the waveforms are such that accuracy standards are generically
not met for signal-to-noise ratios relevant for detection, except for some best
cases using extrapolation from several runs. A detailed analysis of the errors
is thus imperative for the use of numerical relativity waveforms from binary
neutron stars in quantitative studies. The waveforms are compared with the
post-Newtonian Taylor T4 approximants both for point-particle and including the
analytically known tidal corrections. The T4 approximants accumulate
significant phase differences of 2 rad at contact and 4 rad at merger,
underestimating the influence of finite size effects. Tidal signatures in the
waveforms are thus important at least during the last six orbits of the merger
process.Comment: Physical Review D (Vol.85, No.10) 201
All speed scheme for the low mach number limit of the Isentropic Euler equation
An all speed scheme for the Isentropic Euler equation is presented in this
paper. When the Mach number tends to zero, the compressible Euler equation
converges to its incompressible counterpart, in which the density becomes a
constant. Increasing approximation errors and severe stability constraints are
the main difficulty in the low Mach regime. The key idea of our all speed
scheme is the special semi-implicit time discretization, in which the low Mach
number stiff term is divided into two parts, one being treated explicitly and
the other one implicitly. Moreover, the flux of the density equation is also
treated implicitly and an elliptic type equation is derived to obtain the
density. In this way, the correct limit can be captured without requesting the
mesh size and time step to be smaller than the Mach number. Compared with
previous semi-implicit methods, nonphysical oscillations can be suppressed. We
develop this semi-implicit time discretization in the framework of a first
order local Lax-Friedrich (LLF) scheme and numerical tests are displayed to
demonstrate its performances
Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity
A recent paper by Lucas-Serrano et al. indicates that a high-resolution
central (HRC) scheme is robust enough to yield accurate hydrodynamical
simulations of special relativistic flows in the presence of ultrarelativistic
speeds and strong shock waves. In this paper we apply this scheme in full
general relativity (involving {\it dynamical} spacetimes), and assess its
suitability by performing test simulations for oscillations of rapidly rotating
neutron stars and merger of binary neutron stars. It is demonstrated that this
HRC scheme can yield results as accurate as those by the so-called
high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers.
Furthermore, the adopted HRC scheme has increased computational efficiency as
it avoids the costly solution of Riemann problems and has practical advantages
in the modeling of neutron star spacetimes. Namely, it allows simulations with
stiff equations of state by successfully dealing with very low-density
unphysical atmospheres. These facts not only suggest that such a HRC scheme may
be a desirable tool for hydrodynamical simulations in general relativity, but
also open the possibility to perform accurate magnetohydrodynamical simulations
in curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report
A Well-Balanced Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations
We develop a well-balanced central-upwind scheme for rotating shallow water
model with horizontal temperature and/or density gradients---the thermal
rotating shallow water (TRSW). The scheme is designed using the flux
globalization approach: first, the source terms are incorporated into the
fluxes, which results in a hyperbolic system with global fluxes; second, we
apply the Riemann-problem-solver-free central-upwind scheme to the rewritten
system. We ensure that the resulting method is well-balanced by switching off
the numerical diffusion when the computed solution is near (at)
thermo-geostrophic equilibria.
The designed scheme is successfully tested on a series of numerical examples.
Motivated by future applications to large-scale motions in the ocean and
atmosphere, the model is considered on the tangent plane to a rotating planet
both in mid-latitudes and at the Equator. The numerical scheme is shown to be
capable of quite accurately maintaining the equilibrium states in the presence
of nontrivial topography and rotation. Prior to numerical simulations, an
analysis of the TRSW model based on the use of Lagrangian variables is
presented, allowing one to obtain criteria of existence and uniqueness of the
equilibrium state, of the wave-breaking and shock formation, and of instability
development out of given initial conditions. The established criteria are
confirmed in the conducted numerical experiments
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