An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit
- The Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712 (United States)
- Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095 (United States)
We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme.
- OSTI ID:
- 22382170
- Journal Information:
- Journal of Computational Physics, Vol. 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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