13,904 research outputs found
Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
In this paper we discuss the treatment of discontinuities in Smoothed
Particle Hydrodynamics (SPH) simulations. In particular we discuss the
difference between integral and differential representations of the fluid
equations in an SPH context and how this relates to the formulation of dissip
ative terms for the capture of shocks and other discontinuities.
This has important implications for many problems, in particular related to
recently highlighted problems in treating Kelvin-Helmholtz instabilities across
entropy gradients in SPH. The specific problems pointed out by Agertz et al.
(2007) are shown to be related in particular to the (lack of) treatment of
contact discontinuities in standard SPH formulations which can be cured by the
simple application of an artificial thermal conductivity term. We propose a new
formulation of artificial thermal conductivity in SPH which minimises
dissipation away from discontinuities and can therefore be applied quite
generally in SPH calculations.Comment: 31 pages, 10 figures, submitted to J. Comp. Phys. Movies + hires
version available at http://www.astro.ex.ac.uk/people/dprice/pubs/kh/ . v3:
modified as per referee's comments - comparison with Ritchie & Thomas
formulation added, quite a few typos fixed. No major change in metho
Symmetry Breaking for Bosonic Systems on Orbifolds
We discuss a general class of boundary conditions for bosons living in an
extra spatial dimension compactified on S^1/Z_2. Discontinuities for both
fields and their first derivatives are allowed at the orbifold fixed points. We
analyze examples with free scalar fields and interacting gauge vector bosons,
deriving the mass spectrum, that depends on a combination of the twist and the
jumps. We discuss how the same physical system can be characterized by
different boundary conditions, related by local field redefinitions that turn a
twist into a jump or vice-versa. When the description is in term of
discontinuous fields, appropriate lagrangian terms should be localized at the
orbifold fixed points.Comment: 21 pages, 2 figure
Richardson Extrapolation for Linearly Degenerate Discontinuities
In this paper we investigate the use of Richardson extrapolation to estimate
the convergence rates for numerical solutions to advection problems involving
discontinuities. We use modified equation analysis to describe the expectation
of the approach. In general, the results do not agree with a-priori estimates
of the convergence rates. However, we identify one particular use case where
Richardson extrapolation does yield the proper result. We then demonstrate this
result using a number of numerical examples.Comment: 19 pages, 4 figur
A PDE-constrained optimization formulation for discrete fracture network flows
We investigate a new numerical approach for the computation of the 3D flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex 3D systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. Independent meshing process within each fracture is a very important issue for practical large scale simulations making easier mesh generation. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures
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