4,184 research outputs found
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
Universality of the Small-Scale Dynamo Mechanism
We quantify possible differences between turbulent dynamo action in the Sun
and the dynamo action studied in idealized simulations. For this purpose we
compare Fourier-space shell-to-shell energy transfer rates of three
incrementally more complex dynamo simulations: an incompressible, periodic
simulation driven by random flow, a simulation of Boussinesq convection, and a
simulation of fully compressible convection that includes physics relevant to
the near-surface layers of the Sun. For each of the simulations studied, we
find that the dynamo mechanism is universal in the kinematic regime because
energy is transferred from the turbulent flow to the magnetic field from
wavenumbers in the inertial range of the energy spectrum. The addition of
physical effects relevant to the solar near-surface layers, including
stratification, compressibility, partial ionization, and radiative energy
transport, does not appear to affect the nature of the dynamo mechanism. The
role of inertial-range shear stresses in magnetic field amplification is
independent from outer-scale circumstances, including forcing and
stratification. Although the shell-to-shell energy transfer functions have
similar properties to those seen in mean-flow driven dynamos in each simulation
studied, the saturated states of these simulations are not universal because
the flow at the driving wavenumbers is a significant source of energy for the
magnetic field.Comment: 16 pages, 9 figures, accepted for publication in Ap
Tsunami generation by paddle motion and its interaction with a beach: Lagrangian modelling and experiment
A 2D Lagrangian numerical wave model is presented and validated against a set of physical wave-flume experiments on interaction of tsunami waves with a sloping beach. An iterative methodology is proposed and applied for experimental generation of tsunami-like waves using a piston-type wavemaker with spectral control. Three distinct types of wave interaction with the beach are observed with forming of plunging or collapsing breaking waves. The Lagrangian model demonstrates good agreement with experiments. It proves to be efficient in modelling both wave propagation along the flume and initial stages of strongly non-linear wave interaction with a beach involving plunging breaking. Predictions of wave runup are in agreement with both experimental results and the theoretical runup law
Numerical study of the small scale structures in Boussinesq convection
Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate Essentially Nonoscillatory (ENO) scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. The numerical results suggest that the collapse of the bubble cap is unlikely to occur in resolved calculations. The strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. We also found that the cascade of energy to small scales is dominated by the formulation of thin and sharp fronts across which density jumps
Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries
Fourth-order stream-function methods are proposed for the time dependent, incompressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the noslip condition. Formal error analysis is done for a simple model problem, showing that this extrapolation introduces numerical boundary layers at fifth-order in the stream-function. The fourth-order convergence in velocity of the proposed method for the full problem is shown numerically
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