1,670 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 time-stepping for incompressible flow. Part II: Navier-Stokes equations
We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics
Variational Principles for Stochastic Fluid Dynamics
This paper derives stochastic partial differential equations (SPDEs) for
fluid dynamics from a stochastic variational principle (SVP). The Legendre
transform of the Lagrangian formulation of these SPDEs yields their Lie-Poisson
Hamiltonian form. The paper proceeds by: taking variations in the SVP to derive
stochastic Stratonovich fluid equations; writing their It\^o representation;
and then investigating the properties of these stochastic fluid models in
comparison with each other, and with the corresponding deterministic fluid
models. The circulation properties of the stochastic Stratonovich fluid
equations are found to closely mimic those of the deterministic ideal fluid
models. As with deterministic ideal flows, motion along the stochastic
Stratonovich paths also preserves the helicity of the vortex field lines in
incompressible stochastic flows. However, these Stratonovich properties are not
apparent in the equivalent It\^o representation, because they are disguised by
the quadratic covariation drift term arising in the Stratonovich to It\^o
transformation. This term is a geometric generalisation of the quadratic
covariation drift term already found for scalar densities in Stratonovich's
famous 1966 paper. The paper also derives motion equations for two examples of
stochastic geophysical fluid dynamics (SGFD); namely, the Euler-Boussinesq and
quasigeostropic approximations.Comment: 19 pages, no figures, 2nd version. To appear in Proc Roy Soc A.
Comments to author are still welcome
Active and passive fields face to face
The statistical properties of active and passive scalar fields transported by
the same turbulent flow are investigated. Four examples of active scalar have
been considered: temperature in thermal convection, magnetic potential in
two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman
turbulence and potential temperature in surface flows. In the cases of
temperature and vorticity, it is found that the active scalar behavior is akin
to that of its co-evolving passive counterpart. The two other cases indicate
that this similarity is in fact not generic and differences between passive and
active fields can be striking: in two-dimensional magnetohydrodynamics the
magnetic potential performs an inverse cascade while the passive scalar
cascades toward the small-scales; in surface flows, albeit both perform a
direct cascade, the potential temperature and the passive scalar have different
scaling laws already at the level of low-order statistical objects. These
dramatic differences are rooted in the correlations between the active scalar
input and the particle trajectories. The role of such correlations in the issue
of universality in active scalar transport and the behavior of dissipative
anomalies is addressed.Comment: 36 pages, 20 eps figures, for the published version see
http://www.iop.org/EJ/abstract/1367-2630/6/1/07
Fluid flow dynamics under location uncertainty
We present a derivation of a stochastic model of Navier Stokes equations that
relies on a decomposition of the velocity fields into a differentiable drift
component and a time uncorrelated uncertainty random term. This type of
decomposition is reminiscent in spirit to the classical Reynolds decomposition.
However, the random velocity fluctuations considered here are not
differentiable with respect to time, and they must be handled through
stochastic calculus. The dynamics associated with the differentiable drift
component is derived from a stochastic version of the Reynolds transport
theorem. It includes in its general form an uncertainty dependent "subgrid"
bulk formula that cannot be immediately related to the usual Boussinesq eddy
viscosity assumption constructed from thermal molecular agitation analogy. This
formulation, emerging from uncertainties on the fluid parcels location,
explains with another viewpoint some subgrid eddy diffusion models currently
used in computational fluid dynamics or in geophysical sciences and paves the
way for new large-scales flow modelling. We finally describe an applications of
our formalism to the derivation of stochastic versions of the Shallow water
equations or to the definition of reduced order dynamical systems
A stable tensor-based deflection model for controlled fluid simulations
The association between fluids and tensors can be observed in some practical situations, such as diffusion tensor imaging and permeable flow. For simulation purposes, tensors may be used to constrain the fluid flow along specific directions. This work seeks to explore this tensor-fluid relationship and to propose a method to control fluid flow with an orientation tensor field. To achieve our purposes, we expand the mathematical formulation governing fluid dynamics to locally change momentum, deflecting the fluid along intended paths. Building upon classical computer graphics approaches for fluid simulation, the numerical method is altered to accomodate the new formulation. Gaining control over fluid diffusion can also aid on visualization of tensor fields, where the detection and highlighting of paths of interest is often desired. Experiments show that the fluid adequately follows meaningful paths induced by the underlying tensor field, resulting in a method that is numerically stable and suitable for visualization and animation purposes.A associação entre fluidos e tensores pode ser observada em algumas situações práticas, como em ressonância magnética por tensores de difusão ou em escoamento permeável. Para fins de simulação, tensores podem ser usados para restringir o escoamento do fluido ao longo de direções especÃficas. Este trabalho visa explorar esta relação tensor-fluido e propor um método para controlar o escoamento usando um campo de tensores de orientação. Para atingir nossos objetivos, nós expandimos a formulação matemática que governa a dinâmica de fluidos para alterar localmente o momento, defletindo o fluido para trajetórias desejadas. Tomando como base abordagens clássicas para simulação de fluidos em computação gráfica, o método numérico é alterado para acomodar a nova formulação. Controlar o processo de difusão pode também ajudar na visualização de campos tensoriais, onde frequentemente busca-se detectar e realçar caminhos de interesse. Os experimentos realizados mostram que o fluido, induzido pelo campo tensorial subjacente, percorre trajetórias significativas, resultando em um método que é numericamente estável e adequado para fins de visualização e animação
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