7,258 research outputs found
Variational Integrators for Reduced Magnetohydrodynamics
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics
equations with applications to both fusion and astrophysical plasmas,
possessing a noncanonical Hamiltonian structure and consequently a number of
conserved functionals. We propose a new discretisation strategy for these
equations based on a discrete variational principle applied to a formal
Lagrangian. The resulting integrator preserves important quantities like the
total energy, magnetic helicity and cross helicity exactly (up to machine
precision). As the integrator is free of numerical resistivity, spurious
reconnection along current sheets is absent in the ideal case. If effects of
electron inertia are added, reconnection of magnetic field lines is allowed,
although the resulting model still possesses a noncanonical Hamiltonian
structure. After reviewing the conservation laws of the model equations, the
adopted variational principle with the related conservation laws are described
both at the continuous and discrete level. We verify the favourable properties
of the variational integrator in particular with respect to the preservation of
the invariants of the models under consideration and compare with results from
the literature and those of a pseudo-spectral code.Comment: 35 page
Numerical studies towards practical large-eddy simulation
Large-eddy simulation developments and validations are presented for an
improved simulation of turbulent internal flows. Numerical methods are proposed
according to two competing criteria: numerical qualities (precision and
spectral characteristics), and adaptability to complex configurations. First,
methods are tested on academic test-cases, in order to abridge with fundamental
studies. Consistent results are obtained using adaptable finite volume method,
with higher order advection fluxes, implicit grid filtering and "low-cost"
shear-improved Smagorinsky model. This analysis particularly focuses on mean
flow, fluctuations, two-point correlations and spectra. Moreover, it is shown
that exponential averaging is a promising tool for LES implementation in
complex geometry with deterministic unsteadiness. Finally, adaptability of the
method is demonstrated by application to a configuration representative of
blade-tip clearance flow in a turbomachine
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