Objective
The lattice gas automata approach involves constructing drastically simplified microscopic models which, in spite of their schematic nature, give rise to macroscopic behaviour in agreement with what would have been obtained with a more realistic description of the microscopic degrees of freedom. A simplified microdynamics has been developed which conserves the irreducible features that are essential to the emergence of a macroscopic behaviour described by a set of partial differential equations. Amongst the successes of this approach was proof that the density fluctuation correlations observed in the numerical simulations and computed from the lattice gas theory are in agreement with the results obtained in laboratory experiments.
A lattice gas automaton has been constructed for thermal fluids. It contains intrinsic Monte Carlo noise and can be considered (in the same sense as a real fluid) as a reservoir of excitations with wavelengths and frequencies ranging from the microscopic level to the hydrodynamic scale. The model exhibits correct thermohydrodynamic fluctuations.
The technique has been used to develop models for numerical simulations of geophysical processes, such as small scale oceanic fronts and double diffusive instabilities, and of reactive phenomena where it would be well suited for application to surface catalytic reactions.
A study has been carried out on the application of the technique to interactions of vortices in 2 dimensions, where examples range from oceanic fronts to certain types of galaxy. Results suggest that the method should also prove useful in the study of turbulent diffusion.
The axial flow in a starting vortex and the breakdown of a vortex and the transition between bubble type and spiral type breakdown were investigated. The axial flow of a starting vortex generated by a rotating flap with an oblique leaching edge was visualized with fluorescent dyes for various Reynolds numbers. The bubble type vortex breakdown was studied by particle tracking velocimetry to get the 3-dimensional instantaneous velocity distribution of the interior region of the bubble. The bubble type and spiral type breakdown and a transition between them initiated by an artificially generated vortex ring was investigated in a water tunnel. A numerical visualization with streak lines of vortex breakdown resulting from a numerical solution of the Navier-Stokes equations for time dependent 3-dimensional flows is illustrated.
The structure of the 3-dimensional wake of a circular cylinder has been interpreted using a phenomenological model. The Ginzburg-Landau equation has been studied analytically and numerically. The characteristic spatial scale of the wake along the axis of the cylinder has been computed and various aspects of the observed behaviour have been modelled, such as the influence of confinement on the flow, oblique vortex shedding, and the existence of cells.
The essential problem of the transition to tridimensionality in a nonstationary flow has been solved. The main parameter of the study is the reduced length, which is a function of both the aspect ratio and the Reynolds number threshold deviation. An increase of this parameter gives rise to the appearance of more and more spatial modes from the single mode regime to chevrons and oblique shedding.
The different orders of magnitude of the coefficients of the normal form have been deduced from experimental results, for the circular cylinder case. The extension of the model to periodic boundary conditions has been satisfactorily tested in the experimental wake of a ring. Many new features, such as the existence of helices, have been noted.
Two models described by the generic term lattice Boltzmann equation (LBE), the relaxation LBE and the collision LBE, have been studied and compared. Both allow the Galilean invariance and the isotropy to be recovered at the same time for arbitrary density and low viscosity. The numerical stability of the models has been investigated both analytically and by simulation of shock profiles for a 1-dimensional model. For such stiff situations, the stability conditions is more stringent than the one given by the eigenvalues of the linearized collision operator.
The accuracy of the low viscosity limit has been investigated by simulation of the flow in a duct with a sudden symmetric expansion. Results from the relaxation LBE and collision LBE schemes were compared to each other, with experiment, and with standard numerical models, with satisfactory results.
The theory of lattice gases has been investigated for flow around an obstacle, for simple geometries involving steady solutions with 1-dimensional space variation, triangular lattice, and boundary parallel or perpendicular to one link of the lattice.
The possibility of realising liquid to gas transitions in lattice gases has been demonstrated for models with nonlocal exchange of momentum between nodes.
A general polynomial algorithm has been derived to find all the linear invariants of any lattice model, to identify spurious nonphysical invariants.
A lattice gas automoton has been constructed for thermal fluids. It contains intrinsic Monte Carlo noise and can be considered (in the same sense as a real fluid) as a reservoir of excitation with wavelength and frequencies ranging from the microscopic level to the hydrodynamic scale. The model exhibits correct thermohydrodynamic fluctuations.
The lattice Boltzmann equation (LBE) scheme has been applied to fully developed turbulence in Rayleigh Benard convection. The scheme is particularly suitable for parallel processing. Agreement between the probability density function (polf) of the temperature and analytical theory has been verified. The exponential shape of the polf of the temperature field was detected at small Rayleigh number. The scaling laws agreed with the Bolgiano scaling.
The self similar multifractal properties of 3-dimensional fully developed turbulence were studied. Achievements included the first analytical computation of the multifractal spectrum in shell models. the definition of a multifractal signal in terms of wavelet expansion and multiplication processes, and the discovery of a new form of self similarity for turbulent flows.
The main goal of the present project concerns the analysis, via computer simulations and laboratory experiments, of the transition regimes towards developped turbulence. Two-dimensional multiphase flows will be investigated as well as transitions towards three-dimensionality in external flows with arbitrary geometry.
Simulations will be performed with the new cellular automata method. The laboratory experiments will be conducted using advanced techniques ,or optimal control, accurate measurements, and efficient
visualization. The results will be subjected to detailed
comparative analysis, in connection with the most recent theoretical developments.
Lattice gas algorithms will be optimized in order to match the requirements imposed by the electronic components for the further development of dedicated highly parallel 3-D machines.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- social sciences law
- natural sciences mathematics applied mathematics mathematical model
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Coordinator
BRUXELLES
Belgium
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.