Efficient Asymptotic Preserving Deterministic methods for the Boltzmann Equation
Abstract
In this lecture notes we review some recent results concerning the numerical solution of nonlinear collisional kinetic equation. The most well-known example is represented by the Boltzmann equation of rarefied gas dynamics (Cercignani, 1988; Cercignani et al., 1994). Besides other classical examples, like the Landau equation of plasma physics (Landau, 1981), kinetic equations play an important role in modelling granular gases (Bobylev et al., 2000), charged particles in semiconductors (Markowich et al., 1989), neutron transport (Jin et al., 2000) and quantum gases (Escobedo et al., 2003b). More recently applications of kinetic equations have been considered for car traffic flows (Klar and Wegener, 1997), chemotactical movements (Chalub et al., 2004), tumor immune cells competition (Bellomo and Bellouquid, 2004), coagulation-fragmentation processes (Escobedo et al., 2003a), population dynamics (Desvillettes et al., 2004), market economies (Cordier et al., 2005), supply chains (Armbruster et al., 2007), flocking dynamics (Ha and Tadmor, 2008) and many other. For a recent introduction to the Boltzmann equation and related kinetic equations we refer the reader to Degond et al. (2004); Villani (2002), recent applications to biology and socio-economy can be found in Naldi et al. (2010).
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 2011
- Accession Number
- ADA587238
Entities
People
- Giovanni Russo
- Lorenzo Pareschi
Organizations
- University of Ferrara