Numerical simulation of jet-forced flow in a circular reservoir using discrete and random vortex methods

This paper describes a Biot–Savart discrete vortex model for simulating the flow patterns which occur when a single high-velocity inflow jet is used to stir the fluid within a circular container. The first stage of the model consists of conformally mapping the circular perimeter of the container onto a rectangle by means of a Schwarz–Christoffel transformation. A potential flow solution is then obtained for the flow inside the rectangle and this is transformed to give the potential flow inside the circle. In the second stage of the simulation, discrete vortices are added at the inlet of the physical system in order to model the inflow shear layers. Velocity components resulting from the discrete vortices and their images in the walls of the cylinder are superimposed on the uniform potential flow solution. The positions of the vortices are updated using a Lagrangian tracking procedure. Viscous effects are incorporated through the use of random walks. From the results it is shown that the discrete vortex method does predict qualitatively the important features of jet-forced reservoir flow.     

On the modeling of granular traffic flow by the kinetic theory for active particles trend to equilibrium and macroscopic behavior

The modeling of vehicular traffic flow is developed by methods of the discrete mathematical kinetic theory for active particles. The discretization refers to the velocity variable in the case of spatially homogeneity. The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale. Moreover, the modeling approach includes in the state equation of the vehicle an activity variable suitable to model the quality (low or high) of the vehicle-driver system. This paper aims to be the first of a project concerning traffic flow by active particles methods.