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Numerical Analysis Series: An application of the discontinuous Galerkin method to numerical models of kinetic equations.

Thursday, April 14, 3:30PM – 5PM
ACES 6.304

Armando Majorana, Dipartimento di Matematica e Informatica - University of Catania - Italy

We propose new deterministic numerical models, based on the discontinuous Galerkin (DG) method, for solving kinetic equations as the linear or nonlinear Boltzmann equation for rareed gases, the Boltzmamn equation for charge transport in semiconductor, the radiative transport equation. The unknown of these equations is the distribution function, which, in general, depends on time, space coordinates and particle velocity. We are interested to show a partial application of the DG method,which, in general, will give a set of partial dierential equations, where the unknowns are integrals, with respect to the velocity, of the distribution function multiplies assigned test functions and the independent variables are the time and the space coordinates. For instance, a set of partial differential equations is derived and analyzed in the case of the classical nonlinear Boltzmann equation for mono-atomic gases. In this case the model guarantees the conservation of the mass, momentum and energy for homogeneous solutions.

References A. Majorana: A numerical model of the Boltzmann equation related to the discontinuous Galerkin method. Kinetic and Related models, 4, 1 (2011), 139{151.

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