1,180,330 research outputs found
Hoea a mai tōu waka – Claiming spaces for Māori tamariki and rangatahi in cognitive behaviour therapy
Cognitive Behaviour Therapy (CBT) has been shown to be an effective therapeutic intervention for a variety of psychological difficulties for children and youth (Barrett, Healey-Farrell, March, 2004; Stulemeijer, de Jong, Fiselier, Hoogveld, Bleijenberg, 2005; Butler, Chapman, Forman & Beck, 2006). However there is very little literature on its utility with indigenous children or youth, most of the literature has tended to look at “minority” populations and has focused on psychological outcomes (Weersing & Weisz, 2002; McNeil, Capage, Bennett, 2002)
An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations
in more than one space dimension must either confront the challenge of
controlling errors in the discrete divergence of the magnetic field, or else be
faced with nonlinear numerical instabilities. One approach for controlling the
discrete divergence is through a so-called constrained transport method, which
is based on first predicting a magnetic field through a standard finite volume
solver, and then correcting this field through the appropriate use of a
magnetic vector potential. In this work we develop a constrained transport
method for the 3D ideal MHD equations that is based on a high-resolution wave
propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme
developed by Rossmanith [SIAM J. Sci. Comp. 28, 1766 (2006)], and is based on
the high-resolution wave propagation method of Langseth and LeVeque [J. Comp.
Phys. 165, 126 (2000)]. In particular, in our extension we take great care to
maintain the three most important properties of the 2D scheme: (1) all
quantities, including all components of the magnetic field and magnetic
potential, are treated as cell-centered; (2) we develop a high-resolution wave
propagation scheme for evolving the magnetic potential; and (3) we develop a
wave limiting approach that is applied during the vector potential evolution,
which controls unphysical oscillations in the magnetic field. One of the key
numerical difficulties that is novel to 3D is that the transport equation that
must be solved for the magnetic vector potential is only weakly hyperbolic. In
presenting our numerical algorithm we describe how to numerically handle this
problem of weak hyperbolicity, as well as how to choose an appropriate gauge
condition. The resulting scheme is applied to several numerical test cases.Comment: 46 pages, 12 figure
Multidimensional HLLE Riemann solver; Application to Euler and Magnetohydrodynamic Flows
In this work we present a general strategy for constructing multidimensional
Riemann solvers with a single intermediate state, with particular attention
paid to detailing the two-dimensional Riemann solver. This is accomplished by
introducing a constant resolved state between the states being considered,
which introduces sufficient dissipation for systems of conservation laws.
Closed form expressions for the resolved fluxes are also provided to facilitate
numerical implementation. The Riemann solver is proved to be positively
conservative for the density variable; the positivity of the pressure variable
has been demonstrated for Euler flows when the divergence in the fluid
velocities is suitably restricted so as to prevent the formation of cavitation
in the flow.
We also focus on the construction of multidimensionally upwinded electric
fields for divergence-free magnetohydrodynamical flows. A robust and efficient
second order accurate numerical scheme for two and three dimensional Euler and
magnetohydrodynamic flows is presented. The scheme is built on the current
multidimensional Riemann solver. The number of zones updated per second by this
scheme on a modern processor is shown to be cost competitive with schemes that
are based on a one-dimensional Riemann solver. However, the present scheme
permits larger timesteps
A high-order Godunov scheme for global 3D MHD accretion disks simulations. I. The linear growth regime of the magneto-rotational instability
We employ the PLUTO code for computational astrophysics to assess and compare
the validity of different numerical algorithms on simulations of the
magneto-rotational instability in 3D accretion disks. In particular we stress
on the importance of using a consistent upwind reconstruction of the
electro-motive force (EMF) when using the constrained transport (CT) method to
avoid the onset of numerical instabilities. We show that the electro-motive
force (EMF) reconstruction in the classical constrained transport (CT) method
for Godunov schemes drives a numerical instability. The well-studied linear
growth of magneto-rotational instability (MRI) is used as a benchmark for an
inter-code comparison of PLUTO and ZeusMP. We reproduce the analytical results
for linear MRI growth in 3D global MHD simulations and present a robust and
accurate Godunov code which can be used for 3D accretion disk simulations in
curvilinear coordinate systems
A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows
In this paper we present a genuinely two-dimensional HLLC Riemann solver. On
logically rectangular meshes, it accepts four input states that come together
at an edge and outputs the multi-dimensionally upwinded fluxes in both
directions. This work builds on, and improves, our prior work on
two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here
achieves its stabilization by introducing a constant state in the region of
strong interaction, where four one-dimensional Riemann problems interact
vigorously with one another. A robust version of the HLL Riemann solver is
presented here along with a strategy for introducing sub-structure in the
strongly-interacting state. Introducing sub-structure turns the two-dimensional
HLL Riemann solver into a two-dimensional HLLC Riemann solver. The
sub-structure that we introduce represents a contact discontinuity which can be
oriented in any direction relative to the mesh.
The Riemann solver presented here is general and can work with any system of
conservation laws. We also present a second order accurate Godunov scheme that
works in three dimensions and is entirely based on the present multidimensional
HLLC Riemann solver technology. The methods presented are cost-competitive with
traditional higher order Godunov schemes
On the Divergence-Free Condition in Godunov-Type Schemes for Ideal Magnetohydrodynamics: the Upwind Constrained Transport Method
We present a general framework to design Godunov-type schemes for
multidimensional ideal magnetohydrodynamic (MHD) systems, having the
divergence-free relation and the related properties of the magnetic field B as
built-in conditions. Our approach mostly relies on the 'Constrained Transport'
(CT) discretization technique for the magnetic field components, originally
developed for the linear induction equation, which assures div(B)=0 and its
preservation in time to within machine accuracy in a finite-volume setting. We
show that the CT formalism, when fully exploited, can be used as a general
guideline to design the reconstruction procedures of the B vector field, to
adapt standard upwind procedures for the momentum and energy equations,
avoiding the onset of numerical monopoles of O(1) size, and to formulate
approximate Riemann solvers for the induction equation. This general framework
will be named here 'Upwind Constrained Transport' (UCT). To demonstrate the
versatility of our method, we apply it to a variety of schemes, which are
finally validated numerically and compared: a novel implementation for the MHD
case of the second order Roe-type positive scheme by Liu and Lax (J. Comp.
Fluid Dynam. 5, 133, 1996), and both the second and third order versions of a
central-type MHD scheme presented by Londrillo and Del Zanna (Astrophys. J.
530, 508, 2000), where the basic UCT strategies have been first outlined
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