15,877 research outputs found
Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations
We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics
Glimm-Godunov's Method for Cosmic-ray-hydrodynamics
A numerical method for integrating the equations describing a dynamically
coupled system made of a fluid and cosmic-rays is developed. In smooth flows
the effect of CR pressure is accounted for by modification of the
characteristic equations and the energy exchange between cosmic-rays and the
fluid, due to diffusive processes in configuration and momentum space, is
modeled with a flux conserving method. Provided the shock acceleration
efficiency as a function of the upstream conditions and shock Mach number, we
show that the Riemann solver can be modified to take into account the
cosmic-ray mediation without having to resolve the cosmic-ray induced
substructure. Shocks are advanced with Glimm's method which preserves their
discontinuous character without any smearing, thus allowing to maintain
self-consistency in the shock solutions. In smooth flows either Glimm's or a
higher order Godunov's method can be applied, with the latter producing better
results when approximations are introduced in the Riemann solver.Comment: 32 pages, 4 figs, JCP in press, improved description of boundary
conditions at high momenta, references updated, version matching the one
accepted for publicatio
Convective regularization for optical flow
We argue that the time derivative in a fixed coordinate frame may not be the
most appropriate measure of time regularity of an optical flow field. Instead,
for a given velocity field we consider the convective acceleration which describes the acceleration of objects moving according to
. Consequently we investigate the suitability of the nonconvex functional
as a regularization term for optical flow. We
demonstrate that this term acts as both a spatial and a temporal regularizer
and has an intrinsic edge-preserving property. We incorporate it into a
contrast invariant and time-regularized variant of the Horn-Schunck functional,
prove existence of minimizers and verify experimentally that it addresses some
of the problems of basic quadratic models. For the minimization we use an
iterative scheme that approximates the original nonlinear problem with a
sequence of linear ones. We believe that the convective acceleration may be
gainfully introduced in a variety of optical flow models
A Two-moment Radiation Hydrodynamics Module in Athena Using a Time-explicit Godunov Method
We describe a module for the Athena code that solves the gray equations of
radiation hydrodynamics (RHD), based on the first two moments of the radiative
transfer equation. We use a combination of explicit Godunov methods to advance
the gas and radiation variables including the non-stiff source terms, and a
local implicit method to integrate the stiff source terms. We adopt the M1
closure relation and include all leading source terms. We employ the reduced
speed of light approximation (RSLA) with subcycling of the radiation variables
in order to reduce computational costs. Our code is dimensionally unsplit in
one, two, and three space dimensions and is parallelized using MPI. The
streaming and diffusion limits are well-described by the M1 closure model, and
our implementation shows excellent behavior for a problem with a concentrated
radiation source containing both regimes simultaneously. Our operator-split
method is ideally suited for problems with a slowly varying radiation field and
dynamical gas flows, in which the effect of the RSLA is minimal. We present an
analysis of the dispersion relation of RHD linear waves highlighting the
conditions of applicability for the RSLA. To demonstrate the accuracy of our
method, we utilize a suite of radiation and RHD tests covering a broad range of
regimes, including RHD waves, shocks, and equilibria, which show second-order
convergence in most cases. As an application, we investigate radiation-driven
ejection of a dusty, optically thick shell in the interstellar medium (ISM).
Finally, we compare the timing of our method with other well-known iterative
schemes for the RHD equations. Our code implementation, Hyperion, is suitable
for a wide variety of astrophysical applications and will be made freely
available on the Web.Comment: 30 pages, 29 figures, accepted for publication in ApJ
Comparison of different nonlinear solvers for 2D time-implicit stellar hydrodynamics
Time-implicit schemes are attractive since they allow numerical time steps
that are much larger than those permitted by the Courant-Friedrich-Lewy
criterion characterizing time-explicit methods. This advantage comes, however,
with a cost: the solution of a system of nonlinear equations is required at
each time step. In this work, the nonlinear system results from the
discretization of the hydrodynamical equations with the Crank-Nicholson scheme.
We compare the cost of different methods, based on Newton-Raphson iterations,
to solve this nonlinear system, and benchmark their performances against
time-explicit schemes. Since our general scientific objective is to model
stellar interiors, we use as test cases two realistic models for the convective
envelope of a red giant and a young Sun. Focusing on 2D simulations, we show
that the best performances are obtained with the quasi-Newton method proposed
by Broyden. Another important concern is the accuracy of implicit calculations.
Based on the study of an idealized problem, namely the advection of a single
vortex by a uniform flow, we show that there are two aspects: i) the nonlinear
solver has to be accurate enough to resolve the truncation error of the
numerical discretization, and ii) the time step has be small enough to resolve
the advection of eddies. We show that with these two conditions fulfilled, our
implicit methods exhibit similar accuracy to time-explicit schemes, which have
lower values for the time step and higher computational costs. Finally, we
discuss in the conclusion the applicability of these methods to fully implicit
3D calculations.Comment: Accepted for publication in A&
A three-dimensional spectral algorithm for simulations of transition and turbulence
A spectral algorithm for simulating three dimensional, incompressible, parallel shear flows is described. It applies to the channel, to the parallel boundary layer, and to other shear flows with one wall bounded and two periodic directions. Representative applications to the channel and to the heated boundary layer are presented
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