Approximation of the Boltzmann equation by discrete velocity models
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 60K35 76P05 82C40
- Boltzmann equation, discrete velocity models, weak convergence, random mass flow
Two convergence results related to the approximation of the Boltzmann equation by discrete velocity models are presented. First we construct a sequence of deterministic discrete velocity models and prove convergence (as the number of discrete velocities tends to infinity) of their solutions to the solution of a spatially homogeneous Boltzmann equation. Second we introduce a sequence of Markov jump processes (interpreted as random discrete velocity models) and prove convergence (as the intensity of jumps tends to infinity) of these processes to the solution of a deterministic discrete velocity model.
- J. Statist. Phys., 78 (1995), pp. 1555--1570