Serge Huberson

Simulation of anisotropic diffusion by means of a diffusion velocity method

An alternative method to the Particle Strength Exchange method for solving the advection-diffusion equation in the general case of a non-isotropic and non-uniform diffusion is proposed. This method is an extension of the diffusion velocity method. It is shown that this extension is quite straightforward due to the explicit use of the diffusion flux in the expression of the diffusion velocity. This approach is used to simulate pollutant transport in groundwater and the results are compared to those of the PSE method presented in an earlier study by Zimmermann et al.

Vortex particle methods in aeroacoustic calculations

The connection between vortex particle methods and aeroacoustics is considered within the framework of Lighthills acoustic analogy which allows to decouple the flow from noise propagation. For the flow, techniques such as tree-algorithms and the particle-mesh method are brought together with the aim to achieve the best possible performance in view of analyzing complex problems. The flow results are then input to the acoustic wave equation which is solved in integral form. It will involve monopole, dipole and quadrupole terms which can be successively integrated. The significance of such an approach is first demonstrated in two problems, both related to vortex-solid interactions. The first is a generic one and considers the interaction of a vortex filament interacting with a sphere while the second considers helicopter noise as an example of a complex engineering set-up.

Particles and grid

Abstract In this paper, hybrid methods involving particles have been investigated. First, the main characteristics of the particle method are briefly outlined and an example of application to a really complex case is presented. The particle/grid method which is also the basis for mixing particles with other methods is described. The two main alternatives: domain decomposition and perturbation formulation are then discussed and some examples are presented.

From Navier-Stokes to Stokes by means of particle methods

The viscous flow around a circular cylinder was investigated by means of a particle method over a wide Reynolds number range, from 0.0001 to 1000. A special care was devoted to the satisfaction of the no-slip condition which was expressed through a fourth order partial differential equation for the stream function according to the method initially proposed by Achdou and Pironneau. This equation was solved by a boundary integral method which simultaneously satisfied a Dirichlet and a Neumann condition. The algorithm was immersed within a particle method framework and results in a versatile method which can deal with relatively high Reynolds numbers as well as Stokes flows. The numerical results were analysed and compared to those obtained by others numerically, experimentally and even theoretically for the low Reynolds number limit. The behaviour of the method for the two extreme cases was specially investigated.

Coupling particle sets of contours and streamline methods for solving convection problems

In this work a particle sets of contours method is coupled with a streamline technique in order to obtain accurate approximations of transport problems. A modified streamline technique is proposed and several bench tests arising in the field of porous media are then simulated to validate the new method.

Combined Finite Element — Particles Discretisation for Simulation of Transport-Dispersion in Porous Media

Combining finite element together with particle methods provide one of the best compromise for solving transport problem in porous media. Saturated or non-saturated flows are determined by boundary condition and the media permeability. 1For real terrain, permeability can consist in various almost constant and imbricated zones with complex shapes. Thus, it is of some interest that the boundary between two adjacent zones coincides with a natural mesh interface and that each element is entirely contains in one such zone. Beside this, solving transport equation by means of particle methods offers two distinctive advantages. The method is unconditionally stable when applied to a pure convective equation, and it does not contain any numerical diffusion if the particle trajectories are correctly computed. Therefore the combination of finite elements and particle method appears to be a straightforward application of the principle: “the right method at the right place”.

Adapting particle methods to model the dynamics of concentration gradients and chemical reactivity under advective diffusive transport conditions

Concentration organization and dynamics in heterogeneous porous media are key physical factors driving chemical reactivity. At equilibrium, reactivity depends not only on the concentration distribution but also on concentration gradients. As high and low values of concentration and concentration gradient do not superpose, we derive a transport equation for the concentration gradients and set up an adapted particle method to approach them numerically. Particles dynamically optimize their organization to provide highly accurate concentration gradients. The global strategy combining separate particle methods for the concentration and its gradient gives optimal predictions of reactivity.

NUMERICAL STUDY OF SOUND RADIATION BY AXISYMMETRIC VORTEX RINGS

The sound production by vortex rings is investigated by means of an axisymmetric vortex particle method. The predictions are first calibrated by analyzing the noise generated by steady vortex rings that are described by the analytical solutions of Fraenkel and Norbury. The noise produced by isolated vortex rings for both nominally steady and unsteady cores is then analyzed. For nominally steady cores, computed results indicate that the efficiency of sound radiation decreases as the slenderness parameter is reduced, and the acoustic signals reveal a dominant period that is approximately half the eddy turnover time. For unsteady cores, the amplitude of the radiated sound is substantially higher than that of similar steady rings. When the initial core vorticity distribution is nonuniform, complex internal motion may also occur within the core which is also reflected in the corresponding far-field acoustic signal. Finally, the effect of vortex stretching is analyzed based on computations of two coaxial corotating vortex rings.

A New Particle Set of Contours Method for Advection-Diffusion Problems Applied to the Modelling of Waste Disposal

In this work a particle sets of contours method is coupled to a streamline technique in order to obtain accurate approximations of transport problems. A modified streamlines technique is proposed and several bench tests arising in porous media are then simulated to validate the new method. These results are complemented with the resolution of the diffusion operator in a non conservative form where the non-linear diffusion operator is transformed in a velocity-like term and solved using this new particle method. The method is then used to model transport in porous media applied to the waste disposal.

Hybrid Particle Level-Set Method for Convection-Diffusion Problems in Porous Media

In this work a particle level-set method is coupled to a streamline technique in order to obtain accurate approximations of transport-diffusion problems in porous media. The convective part is resolved using a modified streamlines technique and the diffusion is approximated taking advantage from a level-set framework applied to particle methods. Several bench tests are then simulated to validate the new method.