On the maximum time step in weakly compressible SPH

International audienceIn the SPH method for viscous fluids, the time step is subject to empirical stability criteria. We proceed to a stability analysis of the Weakly Compressible SPH equations using the von Neumann approach in arbitrary space dimension for unbounded flow. Considering the continuous SPH interpolant based on integrals, we obtain a theoretical stability criterion for the time step, depending on the kernel standard deviation, the speed of sound and the viscosity. The stability domain appears to be almost independent of the kernel choice for a given space discretisation. Numerical tests show that the theory is very accurate, despite the approximations made. We then extend the theory in order to study the influence of the method used to compute the density, of the gradient and divergence SPH operators, of background pressure, of the model used for viscous forces and of a constant velocity gradient. The influence of time integration scheme is also studied, and proved to be prominent. All of the above theoretical developments give excellent agreement against numerical results. It is found that velocity gradients almost do not affect stability, provided some background pressure is used. Finally, the case of bounded flows is briefly addressed from numerical tests in three cases: a laminar Poiseuille flow in a pipe, a lid-driven cavity and the collapse of a water column on a wedge

An overview on the capabilities of the TELEMACMASCARET system to deal with tsunamis: feedbacks from TANDEM project

Water Qualit

Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH

International audienceThis work aims at improving the 2-D incompressible SPH model (ISPH) by adapting it to the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [10]. The ISPH algorithm considered is as proposed by Lind et al. [25], based on the projection method with a divergence-free velocity field and using a stabilising procedure based on particle shifting. However, we consider an extension of this model to Reynolds-Averaged Navier-Stokes equations based on the k- turbulent closure model, as done in [10]. The discrete SPH operators are modified by the new description of the wall boundary conditions. In particular, a boundary term appears in the Laplacian operator, which makes it possible to accurately impose a von Neumann pressure wall boundary condition that corresponds to impermeability. The shifting and free-surface detection algorithms have also been adapted to the new boundary conditions. Moreover, a new way to compute the wall renormalisation factor in the frame of the unified semi-analytical boundary conditions is proposed in order to decrease the computational time. We present several verifications to the present approach, including a lid-driven cavity, a water column collapsing on a wedge and a periodic schematic fish-pass. Our results are compared to Finite Volumes methods, using Volume of Fluids in the case of free-surface flows. We briefly investigate the convergence of the method and prove its ability to model complex free-surface and turbulent flows. The results are generally improved when compared to a weakly compressible SPH model with the same boundary conditions, especially in terms of pressure prediction

Diffusion in grid turbulence of isotropic macro-particles using a Lagrangian stochastic method: theory and validation.

The prediction of solid bodies transport (such as algae, debris, sediment grains, or corrosion deposits) is a necessary requirement in many industrial or environmental processes. The physical processes involved cover a wide range of processes, from tidal flow to turbulent eddies and particle drag. A stochastic model was therefore developed to link the different scales of the physical processes where it was assumed that the particles are dilute enough that they do not affect the flow or the motion of other particles while being large enough that each particle does not follow exactly the fluid motions (i.e., macro-particles). The stochastic model is built in such a way that it uses Reynolds-averaged fluid properties to predict trajectories of individual particles. This model was then tested using experimental measurements obtained for isotropic particles released in semi-homogeneous turbulence. The turbulent flow was generated using a pair of oscillating grids and was characterized using particle image velocimetry measurements. The trajectories of the particles were measured using a pair of high resolution cameras. The comparison between the experimental data and different numerical models gives satisfactory results

Un couplage fluide-fluide de type Boussinesq-SPH pour des calculs à proximité de structures hydroliennes

National audienceAu cours de notre exposé, nous présenterons une stratégie de couplage pour des problèmes d'écoulements à surface libre. L'objectif est ici, par exemple, de prendre en compte la propagation de vagues sur des distances moyennes à grandes, et leur déferlement sur les côtes à une échelle plus réduite

Coupling SPH with a 1-D Boussinesq-type wave model

International audienceThe high computational cost of SPH remains problematic in dealing with wave propagation, especially when the domains considered are large. In order to overcome this difficulty, we propose to couple 2-D SPH with a 1-D Finite Difference Boussinesq-type model. The latter deals with wave propagations for most of the spatial domain, whereas SPH computations focus on the shoreline or close to off-shore structures, where a complex description of the free-surface is required. The re-use of existing codes is achieved using a generic implementation based on Component Technology. The communication between software is ensured by the middleware Component Template Library (CTL). In order to deal with open domains, open-boundaries have to be implemented for SPH, with water height and velocity varying in space and time. These velocity and water height values are then driven by the Boussinesq-type model. As an illustration of the one way coupling, we present herein two simple examples of water waves, the first one with a flat bottom, the other one representing a schematic coastal protection

Transport of isotropic particles in a partially obstructed channel flow

The transport of particles in turbulent flows is a common problem in hydraulic engineering. In this paper, the focus is set on a numerical model used to simulate the transport of small bodies (debris, algae, etc.) along a coastline. In this problem, the particles are larger than the small turbulent eddies, but smaller than the large turbulent eddies, and sufficiently diluted within the flow so that each particle does not affect the flow or the motion of other particles. A mixed Eulerian-Lagrangian approach was chosen in order to model a large flow area with sufficient information for the turbulent diffusion. This model is validated through an experiment on particles released into a partially obstructed channel flow. The measurements are then compared with simulations using two Eulerian industrial codes, Telemac-2D and OpenFoam. Finally, an application to algae bloom transport in a harbour is presented