6 research outputs found
A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization
A deterministic method is proposed for solving the Boltzmann equation. The
method employs a Galerkin discretization of the velocity space and adopts, as
trial and test functions, the collocation basis functions based on weights and
roots of a Gauss-Hermite quadrature. This is defined by means of half- and/or
full-range Hermite polynomials depending whether or not the distribution
function presents a discontinuity in the velocity space. The resulting
semi-discrete Boltzmann equation is in the form of a system of hyperbolic
partial differential equations whose solution can be obtained by standard
numerical approaches. The spectral rate of convergence of the results in the
velocity space is shown by solving the spatially uniform homogeneous relaxation
to equilibrium of Maxwell molecules. As an application, the two-dimensional
cavity flow of a gas composed by hard-sphere molecules is studied for different
Knudsen and Mach numbers. Although computationally demanding, the proposed
method turns out to be an effective tool for studying low-speed slightly
rarefied gas flows
Toward a Mathematical Theory of Behavioral-Social Dynamics for Pedestrian Crowds
This paper presents a new approach to behavioral-social dynamics of
pedestrian crowds by suitable development of methods of the kinetic theory. It
is shown how heterogeneous individual behaviors can modify the collective
dynamics, as well as how local unusual behaviors can propagate in the crowd.
The main feature of this approach is a detailed analysis of the interactions
between dynamics and social behaviors.Comment: 22 pages, 5 figure