In this work two particle methods are studied in the context of viscous flows. The first one is a Vortex Particle Method, called Diffused Vortex Hydrodynamics (DVH), recently developed to simulate complex viscous flows at medium and high Reynolds regimes. This method presents some similarities with the SPH model and its Lagrangian meshless nature, even if it is based on a different numerical approach. Advantages and drawbacks of the two methods have been previously studied in Colagrossi et al. [1] from a theoretical point of view and in Rossi et al. [2], where these particle methods have been tested on selected benchmarks. Further investigations are presented in this article highlighting analogies and differences between the two particle models.

In nature, when hazardous geophysical granular flows (e.g. a snow avalanche) impact on an obstacle as they stream down a slope, rapid changes in flow depth, direction and velocity will occur. It is important to understand how granular material flows around such obstacles in order to enhance the design of defense structures. In this study, a three dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) model is developed to simulate granular flow past different types of obstacles. The elastic–perfectly plastic model with implementation of the Mohr–Coulomb failure criterion is applied to simulate the material behavior, which describes the stress states of soil in the plastic flow regime. The model was validated by simulating the collapse of a 3-D column of sand with two different aspect ratios; the results showed that the SPH method is capable of simulating granular flow. The model is then applied to simulate the gravity-driven granular flow down an inclined surface obstructed by a group of columns with different spacing, a circular cylinder and a tetrahedral wedge. The numerical results are then compared with experimental results and two different numerical solutions. The good agreements obtained from these comparisons demonstrate that the SPH method may be a powerful method for simulating granular flow and can be extended to design protective structures.

A new Particle Vortex Method, called Diffused Vortex Hydrodynamics (DVH), is presented in this paper. The DVH is a meshless method characterized by the use of a regular distribution of points close to a solid surface to perform the vorticity diffusion process in the boundary layer regions. This redistribution avoids excessive clustering or rarefaction of the vortex particles providing robustness and high accuracy to the method. The generation of the regular distribution of points is performed through a packing algorithm which is embedded in the solver. The packing algorithm collocates points regularly around body of arbitrary shape allowing an exact enforcement on the solid surfaces of the no-slip boundary condition. The present method is tested and validated on different problems of increasing complexities up to flows with Reynolds number equal to 100,000 (without using any subgrid-scale turbulence model).

This paper is devoted to the definition, analysis and implementation of semi-Lagrangian methods as they result from particle methods combined with remeshing. We give a complete consistency analysis of these methods, based on the regularity and momentum properties of the remeshing kernels, and a stability analysis of a large class of second and fourth order methods. This analysis is supplemented by numerical illustrations. We also describe a general approach to implement these methods in the context of hybrid computing and investigate their performance on GPU processors as a function of their order of accuracy.

The purpose of this paper is to apply particle methods to the numerical solution of theEPDiff equation. The weak solutions of EPDiff are contact discontinuities that carrymomentum so that wavefront interactions represent collisions in which momentum isexchanged. This behavior allows for the description of many rich physical applications,but also introduces difficult numerical challenges. We present a particle method for theEPDiff equation that is well-suited for this class of solutions and for simulatingcollisions between wavefronts. Discretization by means of the particle method is shown topreserve the basic Hamiltonian, the weak and variational structure of the originalproblem, and to respect the conservation laws associated with symmetry under the Euclideangroup. Numerical results illustrate that the particle method has superior features in bothone and two dimensions, and can also be effectively implemented when the initial data ofinterest lies on a submanifold.

A new criterion is presented to detect global convergence to steady state, and to identify local transient characteristics, during rarefied gas flow simulations performed using the direct simulation Monte Carlo (DSMC) method. Unlike deterministic computational fluid dynamics (CFD) schemes, DSMC is generally subject to large statistical scatter in instantaneous flow property evaluations, which prevents the use of residual tracking procedures as are often employed in CFD simulations. However, reliable prediction of the time to reach steady state is necessary for initialization of DSMC sampling operations. Techniques currently used in DSMC to identify steady state convergence are usually insensitive to weak transient behavior in small regions of relatively low density or recirculating flow. The proposed convergence criterion is developed with the goal of properly identifying such weak transient behavior, while adding negligible computational expense and allowing simple implementation in any existing DSMC code. Benefits of the proposed technique over existing convergence detection methods are demonstrated for representative nozzle/plume expansion flow, hypersonic blunt body flow and driven cavity flow problems.

This work aims at introducing modelling, theoretical and numerical studies related to a new downscaling technique applied to computational fluid dynamics.Our method consists in building a local model, forced by large scale information computed thanks to a classical numerical weather predictor.The local model, compatible with the Navier-Stokes equations, is usedfor the small scale computation (downscaling) of the consideredfluid. It isinspired by Pope's works on turbulence, and consists in a so-called Langevin system of stochastic differential equations. We introduce this model and exhibit its links with classical RANS models. Well-posedness, as well as mean-field interacting particle approximations and boundary condition issues are addressed. We present the numerical discretization of the stochastic downscaling method and investigate the accuracy of the proposed algorithm on simplified situations.