2,448 research outputs found
Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review
Immersed boundary methods for computing confined fluid and plasma flows in
complex geometries are reviewed. The mathematical principle of the volume
penalization technique is described and simple examples for imposing Dirichlet
and Neumann boundary conditions in one dimension are given. Applications for
fluid and plasma turbulence in two and three space dimensions illustrate the
applicability and the efficiency of the method in computing flows in complex
geometries, for example in toroidal geometries with asymmetric poloidal
cross-sections.Comment: in Journal of Plasma Physics, 201
Adaptive multiresolution computations applied to detonations
A space-time adaptive method is presented for the reactive Euler equations
describing chemically reacting gas flow where a two species model is used for
the chemistry. The governing equations are discretized with a finite volume
method and dynamic space adaptivity is introduced using multiresolution
analysis. A time splitting method of Strang is applied to be able to consider
stiff problems while keeping the method explicit. For time adaptivity an
improved Runge--Kutta--Fehlberg scheme is used. Applications deal with
detonation problems in one and two space dimensions. A comparison of the
adaptive scheme with reference computations on a regular grid allow to assess
the accuracy and the computational efficiency, in terms of CPU time and memory
requirements.Comment: Zeitschrift f\"ur Physicalische Chemie, accepte
Wavelet transforms and their applications to MHD and plasma turbulence: a review
Wavelet analysis and compression tools are reviewed and different
applications to study MHD and plasma turbulence are presented. We introduce the
continuous and the orthogonal wavelet transform and detail several statistical
diagnostics based on the wavelet coefficients. We then show how to extract
coherent structures out of fully developed turbulent flows using wavelet-based
denoising. Finally some multiscale numerical simulation schemes using wavelets
are described. Several examples for analyzing, compressing and computing one,
two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201
Self-organization and symmetry-breaking in two-dimensional plasma turbulence
The spontaneous self-organization of two-dimensional magnetized plasma is
investigated within the framework of magnetohydrodynamics with a particular
emphasis on the symmetry-breaking induced by the shape of the confining
boundaries. This symmetry-breaking is quantified by the angular momentum, which
is shown to be generated rapidly and spontaneously from initial conditions free
from angular momentum as soon as the geometry lacks axisymmetry. This effect is
illustrated by considering circular, square, and elliptical boundaries. It is
shown that the generation of angular momentum in nonaxisymmetric geometries can
be enhanced by increasing the magnetic pressure. The effect becomes stronger at
higher Reynolds numbers. The generation of magnetic angular momentum (or
angular field), previously observed at low Reynolds numbers, becomes weaker at
larger Reynolds numbers
Divergence and convergence of inertial particles in high Reynolds number turbulence
Inertial particle data from three-dimensional direct numerical simulations of
particle-laden homogeneous isotropic turbulence at high Reynolds number are
analyzed using Voronoi tessellation of the particle positions, considering
different Stokes numbers. A finite-time measure to quantify the divergence of
the particle velocity by determining the volume change rate of the Voronoi
cells is proposed. For inertial particles the probability distribution function
(PDF) of the divergence deviates from that for fluid particles. Joint PDFs of
the divergence and the Voronoi volume illustrate that the divergence is most
prominent in cluster regions and less pronounced in void regions. For larger
volumes the results show negative divergence values which represent cluster
formation (i.e. particle convergence) and for small volumes the results show
positive divergence values which represents cluster destruction/void formation
(i.e. particle divergence). Moreover, when the Stokes number increases the
divergence takes larger values, which gives some evidence why fine clusters are
less observed for large Stokes numbers. Theoretical analyses further show that
the divergence for random particles in random flow satisfies a PDF
corresponding to the ratio of two independent variables following normal and
gamma distributions in one dimension. Extending this model to three dimensions,
the predicted PDF agrees reasonably well with Monte-Carlo simulations and DNS
data of fluid particles.Comment: 23 pages, 9 figure
Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions
We study the properties of an approximation of the Laplace operator with
Neumann boundary conditions using volume penalization. For the one-dimensional
Poisson equation we compute explicitly the exact solution of the penalized
equation and quantify the penalization error. Numerical simulations using
finite differences allow then to assess the discretisation and penalization
errors. The eigenvalue problem of the penalized Laplace operator with Neumann
boundary conditions is also studied. As examples in two space dimensions, we
consider a Poisson equation with Neumann boundary conditions in rectangular and
circular domains
Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry
We develop a volume penalization method for inhomogeneous Neumann boundary
conditions, generalizing the flux-based volume penalization method for
homogeneous Neumann boundary condition proposed by Kadoch et al. [J. Comput.
Phys. 231 (2012) 4365]. The generalized method allows us to model scalar flux
through walls in geometries of complex shape using simple, e.g. Cartesian,
domains for solving the governing equations. We examine the properties of the
method, by considering a one-dimensional Poisson equation with different
Neumann boundary conditions. The penalized Laplace operator is discretized by
second order central finite-differences and interpolation. The discretization
and penalization errors are thus assessed for several test problems.
Convergence properties of the discretized operator and the solution of the
penalized equation are analyzed. The generalized method is then applied to an
advection-diffusion equation coupled with the Navier-Stokes equations in an
annular domain which is immersed in a square domain. The application is
verified by numerical simulation of steady free convection in a concentric
annulus heated through the inner cylinder surface using an extended square
domain.Comment: 32 pages, 19 figure
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