66,450 research outputs found
Smoothed Particle Magnetohydrodynamics III. Multidimensional tests and the div B = 0 constraint
In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have
described an algorithm for solving the equations of Magnetohydrodynamics (MHD)
using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses
dissipative terms in order to capture shocks and has been tested on a wide
range of one dimensional problems in both adiabatic and isothermal MHD. In this
paper we investigate multidimensional aspects of the algorithm, refining many
of the aspects considered in papers I and II and paying particular attention to
the code's ability to maintain the div B = 0 constraint associated with the
magnetic field. In particular we implement a hyperbolic divergence cleaning
method recently proposed by Dedner et al. (2002) in combination with the
consistent formulation of the MHD equations in the presence of non-zero
magnetic divergence derived in papers I and II. Various projection methods for
maintaining the divergence-free condition are also examined. Finally the
algorithm is tested against a wide range of multidimensional problems used to
test recent grid-based MHD codes. A particular finding of these tests is that
in SPMHD the magnitude of the divergence error is dependent on the number of
neighbours used to calculate a particle's properties and only weakly dependent
on the total number of particles. Whilst many improvements could still be made
to the algorithm, our results suggest that the method is ripe for application
to problems of current theoretical interest, such as that of star formation.Comment: Here is the latest offering in my quest for a decent SPMHD algorithm.
26 pages, 15 figures, accepted for publication in MNRAS. Version with high
res figures available from
http://www.astro.ex.ac.uk/people/dprice/pubs/spmhd/spmhdpaper3.pd
Diffuse LEED intensities of disordered crystal surfaces : III. LEED investigation of the disordered (110) surface of gold
The LEED pattern of clean (101) surfaces of Au show a characteristic (1 × 2) superstructure. The diffuseness of reflections in the reciprocal [010] direction is caused by one-dimensional disorder of chains, strictly ordered into spatial [10 ] direction. There is a transition from this disordered superstructure to the normal (1 × 1) structure at 420 + 15°C. The angular profiles of the and (01) beam are measured at various temperatures and with constant energy and angles of incidence of the primary beam. The beam profiles are deconvoluted approximately with the instrument response function
Study of second order upwind differencing in a recirculating flow
The accuracy and stability of the second order upwind differencing scheme was investigated. The solution algorithm employed is based on a coupled solution of the nonlinear finite difference equations by the multigrid technique. Calculations have been made of the driven cavity flow for several Reynolds numbers and finite difference grids. In comparison with the hybrid differencing, the second order upwind differencing is somewhat more accurate but it is not monotonically accurate with mesh refinement. Also, the convergence of the solution algorithm deteriorates with the use of the second order upwind differencing
Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations
We present a suite of Mathematica-based computer-algebra packages, termed
"Kranc", which comprise a toolbox to convert (tensorial) systems of partial
differential evolution equations to parallelized C or Fortran code. Kranc can
be used as a "rapid prototyping" system for physicists or mathematicians
handling very complicated systems of partial differential equations, but
through integration into the Cactus computational toolkit we can also produce
efficient parallelized production codes. Our work is motivated by the field of
numerical relativity, where Kranc is used as a research tool by the authors. In
this paper we describe the design and implementation of both the Mathematica
packages and the resulting code, we discuss some example applications, and
provide results on the performance of an example numerical code for the
Einstein equations.Comment: 24 pages, 1 figure. Corresponds to journal versio
Smoothed Particle Hydrodynamics and Magnetohydrodynamics
This paper presents an overview and introduction to Smoothed Particle
Hydrodynamics and Magnetohydrodynamics in theory and in practice. Firstly, we
give a basic grounding in the fundamentals of SPH, showing how the equations of
motion and energy can be self-consistently derived from the density estimate.
We then show how to interpret these equations using the basic SPH interpolation
formulae and highlight the subtle difference in approach between SPH and other
particle methods. In doing so, we also critique several `urban myths' regarding
SPH, in particular the idea that one can simply increase the `neighbour number'
more slowly than the total number of particles in order to obtain convergence.
We also discuss the origin of numerical instabilities such as the pairing and
tensile instabilities. Finally, we give practical advice on how to resolve
three of the main issues with SPMHD: removing the tensile instability,
formulating dissipative terms for MHD shocks and enforcing the divergence
constraint on the particles, and we give the current status of developments in
this area. Accompanying the paper is the first public release of the NDSPMHD
SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD
algorithms that can be used to test many of the ideas and used to run all of
the numerical examples contained in the paper.Comment: 44 pages, 14 figures, accepted to special edition of J. Comp. Phys.
on "Computational Plasma Physics". The ndspmhd code is available for download
from http://users.monash.edu.au/~dprice/ndspmhd
- …