6,425 research outputs found
Numerical Models of Binary Neutron Star System Mergers. I.: Numerical Methods and Equilibrium Data for Newtonian Models
The numerical modeling of binary neutron star mergers has become a subject of
much interest in recent years. While a full and accurate model of this
phenomenon would require the evolution of the equations of relativistic
hydrodynamics along with the Einstein field equations, a qualitative study of
the early stages on inspiral can be accomplished by either Newtonian or
post-Newtonian models, which are more tractable. In this paper we offer a
comparison of results from both rotating and non-rotating (inertial) frame
Newtonian calculations. We find that the rotating frame calculations offer
significantly improved accuracy as compared with the inertial frame models.
Furthermore, we show that inertial frame models exhibit significant and
erroneous angular momentum loss during the simulations that leads to an
unphysical inspiral of the two neutron stars. We also examine the dependence of
the models on initial conditions by considering initial configurations that
consist of spherical neutron stars as well as stars that are in equilibrium and
which are tidally distorted. We compare our models those of Rasio & Shapiro
(1992,1994a) and New & Tohline (1997). Finally, we investigate the use of the
isolated star approximation for the construction of initial data.Comment: 32 pages, 19 gif figures, manuscript with postscript figures
available at http://www.astro.sunysb.edu/dswesty/docs/nspap1.p
The fully-implicit log-conformation formulation and its application to three-dimensional flows
The stable and efficient numerical simulation of viscoelastic flows has been
a constant struggle due to the High Weissenberg Number Problem. While the
stability for macroscopic descriptions could be greatly enhanced by the
log-conformation method as proposed by Fattal and Kupferman, the application of
the efficient Newton-Raphson algorithm to the full monolithic system of
governing equations, consisting of the log-conformation equations and the
Navier-Stokes equations, has always posed a problem. In particular, it is the
formulation of the constitutive equations by means of the spectral
decomposition that hinders the application of further analytical tools.
Therefore, up to now, a fully monolithic approach could only be achieved in two
dimensions, as, e.g., recently shown in [P. Knechtges, M. Behr, S. Elgeti,
Fully-implicit log-conformation formulation of constitutive laws, J.
Non-Newtonian Fluid Mech. 214 (2014) 78-87].
The aim of this paper is to find a generalization of the previously made
considerations to three dimensions, such that a monolithic Newton-Raphson
solver based on the log-conformation formulation can be implemented also in
this case. The underlying idea is analogous to the two-dimensional case, to
replace the eigenvalue decomposition in the constitutive equation by an
analytically more "well-behaved" term and to rely on the eigenvalue
decomposition only for the actual computation. Furthermore, in order to
demonstrate the practicality of the proposed method, numerical results of the
newly derived formulation are presented in the case of the sedimenting sphere
and ellipsoid benchmarks for the Oldroyd-B and Giesekus models. It is found
that the expected quadratic convergence of Newton's method can be achieved.Comment: 21 pages, 9 figure
Composing Scalable Nonlinear Algebraic Solvers
Most efficient linear solvers use composable algorithmic components, with the
most common model being the combination of a Krylov accelerator and one or more
preconditioners. A similar set of concepts may be used for nonlinear algebraic
systems, where nonlinear composition of different nonlinear solvers may
significantly improve the time to solution. We describe the basic concepts of
nonlinear composition and preconditioning and present a number of solvers
applicable to nonlinear partial differential equations. We have developed a
software framework in order to easily explore the possible combinations of
solvers. We show that the performance gains from using composed solvers can be
substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table
Subspace Acceleration for a Sequence of Linear Systems and Application to Plasma Simulation
We present an acceleration method for sequences of large-scale linear
systems, such as the ones arising from the numerical solution of time-dependent
partial differential equations coupled with algebraic constraints. We discuss
different approaches to leverage the subspace containing the history of
solutions computed at previous time steps in order to generate a good initial
guess for the iterative solver. In particular, we propose a novel combination
of reduced-order projection with randomized linear algebra techniques, which
drastically reduces the number of iterations needed for convergence. We analyze
the accuracy of the initial guess produced by the reduced-order projection when
the coefficients of the linear system depend analytically on time. Extending
extrapolation results by Demanet and Townsend to a vector-valued setting, we
show that the accuracy improves rapidly as the size of the history increases, a
theoretical result confirmed by our numerical observations. In particular, we
apply the developed method to the simulation of plasma turbulence in the
boundary of a fusion device, showing that the time needed for solving the
linear systems is significantly reduced
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