Stochastic representation of the Reynolds transport theorem: revisiting large-scale modeling

We explore the potential of a formulation of the Navier-Stokes equations incorporating a random description of the small-scale velocity component. This model, established from a version of the Reynolds transport theorem adapted to a stochastic representation of the flow, gives rise to a large-scale description of the flow dynamics in which emerges an anisotropic subgrid tensor, reminiscent to the Reynolds stress tensor, together with a drift correction due to an inhomogeneous turbulence. The corresponding subgrid model, which depends on the small scales velocity variance, generalizes the Boussinesq eddy viscosity assumption. However, it is not anymore obtained from an analogy with molecular dissipation but ensues rigorously from the random modeling of the flow. This principle allows us to propose several subgrid models defined directly on the resolved flow component. We assess and compare numerically those models on a standard Green-Taylor vortex flow at Reynolds 1600. The numerical simulations, carried out with an accurate divergence-free scheme, outperform classical large-eddies formulations and provides a simple demonstration of the pertinence of the proposed large-scale modeling

Monte Carlo fixed-lag smoothing in state-space models

This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particle approximation of the filtering and smoothing distributions, the method relies on a simulation technique of conditioned diffusions. The proposed sequential smoother can be applied to general nonlinear and multidimensional models, like the ones used in environmental applications. The smoothing of a turbulent flow in a high-dimensional context is given as a practical example

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

International audienceIn this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows. Both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a Galerkin projection of the Navier Stokes equation. The techniques proposed di er in the control variables they involve. The first one introduces a weak dynamical model defined only up to an additional uncertainty time-dependent function whereas the second one, handles a strong dynamical constraint in which the dynamical system's coe cients constitute the control variables. Both choices correspond to di erent approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction. The techniques have been assessed on numerical data and for real experimental conditions with noisy Image Velocimetry data

A Variational Technique for Time Consistent Tracking of Curves and Motion

In this paper, a new framework for the tracking of closed curves and their associated motion fields is described. The proposed method enables a continuous tracking along an image sequence of both a deformable curve and its velocity field. Such an approach is formalized through the minimization of a global spatio-temporal continuous cost functional, w.r.t a set of variables representing the curve and its related motion field. The resulting minimization process relies on optimal control approach and consists in a forward integration of an evolution law followed by a backward integration of an adjoint evolution model. This latter pde includes a term related to the discrepancy between the current estimation of the state variable and discrete noisy measurements of the system. The closed curves are represented through implicit surface modeling, whereas the motion is described either by a vector field or through vorticity and divergence maps depending on the kind of targeted applications. The efficiency of the approach is demonstrated on two types of image sequences showing deformable objects and fluid motions

A Multigrid Approach for Hierarchical Motion Estimation

This paper focuses on the estimation of the apparent motion field between two consecutive frames in an image sequence. The approach developed here is a tradeoff between methods based on global parameterized flow models and local dense optic flow estimators. The method relies on an adaptive multigrid minimization approach. In addition to accelerated convergence toward good estimates, it allows to mix different parameterizations of the estimate relative to adaptive partitions of the image. The performances of the resulting algorithms are demonstrated in the difficult context of a non-convex energy. Experimental results on real world Meteosat sequences are presented. 1 Introduction Energy-based models constitute a powerful way to cope with low-level image processing problems. These methods are issued either from continuous formalism such as PDEs or from discrete modelization such as Markov random fields. When the energy is convex one can seek the unique minimum with deterministic descen..