5,429 research outputs found
High-order Discretization of a Gyrokinetic Vlasov Model in Edge Plasma Geometry
We present a high-order spatial discretization of a continuum gyrokinetic
Vlasov model in axisymmetric tokamak edge plasma geometries. Such models
describe the phase space advection of plasma species distribution functions in
the absence of collisions. The gyrokinetic model is posed in a four-dimensional
phase space, upon which a grid is imposed when discretized. To mitigate the
computational cost associated with high-dimensional grids, we employ a
high-order discretization to reduce the grid size needed to achieve a given
level of accuracy relative to lower-order methods. Strong anisotropy induced by
the magnetic field motivates the use of mapped coordinate grids aligned with
magnetic flux surfaces. The natural partitioning of the edge geometry by the
separatrix between the closed and open field line regions leads to the
consideration of multiple mapped blocks, in what is known as a mapped
multiblock (MMB) approach. We describe the specialization of a more general
formalism that we have developed for the construction of high-order,
finite-volume discretizations on MMB grids, yielding the accurate evaluation of
the gyrokinetic Vlasov operator, the metric factors resulting from the MMB
coordinate mappings, and the interaction of blocks at adjacent boundaries. Our
conservative formulation of the gyrokinetic Vlasov model incorporates the fact
that the phase space velocity has zero divergence, which must be preserved
discretely to avoid truncation error accumulation. We describe an approach for
the discrete evaluation of the gyrokinetic phase space velocity that preserves
the divergence-free property to machine precision
Computational methods for internal flows with emphasis on turbomachinery
Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed
Non-linear dynamics of Kelvin-Helmholtz unstable magnetized jets: three-dimensional effects
A numerical study of the Kelvin-Helmholtz instability in compressible
magnetohydrodynamics is presented. The three-dimensional simulations consider
shear flow in a cylindrical jet configuration, embedded in a uniform magnetic
field directed along the jet axis. The growth of linear perturbations at
specified poloidal and axial mode numbers demonstrate intricate non-linear
coupling effects. The physical mechanims leading to induced secondary
Kelvin-Helmholtz instabilities at higher mode numbers are identified. The
initially weak magnetic field becomes locally dominant in the non-linear
dynamics before and during saturation. Thereby, it controls the jet deformation
and eventual breakup. The results are obtained using the Versatile Advection
Code [G. Toth, Astrophys. Lett. Comm. 34, 245 (1996)], a software package
designed to solve general systems of conservation laws. An independent
calculation of the same Kelvin-Helmholtz unstable jet configuration using a
three-dimensional pseudo-spectral code gives important insights into the
coupling and excitation events of the various linear mode numbers.Comment: 10 (+7) pages, 6 figures, accepted for Phys. Plasmas 6, to appear
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