TY - JOUR

T1 - An asymptotic-preserving scheme for the semiconductor boltzmann equation with two-scale collisions

T2 - A splitting approach

AU - Hu, Jingwei

AU - Jin, Shi

AU - Wang, Li

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We present a new asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions - a leading-order elastic collision together with a lower-order interparticle collision. When the mean free path is small, numerically solving this equation is prohibitively expensive due to the stiff collision terms. Furthermore, since the equilibrium solution is a (zero-momentum) Fermi-Dirac distribution resulting from joint action of both collisions, the simple BGK penalization designed for the one-scale collision [10] cannot capture the correct energy-transport limit. This problem was addressed in [13], where a thresholded BGK penalization was introduced. Here we propose an alternative based on a splitting approach. It has the advantage of treating the collisions at different scales separately, hence is free of choosing threshold and easier to implement. Formal asymptotic analysis and numerical results validate the effciency and accuracy of the proposed scheme.

AB - We present a new asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions - a leading-order elastic collision together with a lower-order interparticle collision. When the mean free path is small, numerically solving this equation is prohibitively expensive due to the stiff collision terms. Furthermore, since the equilibrium solution is a (zero-momentum) Fermi-Dirac distribution resulting from joint action of both collisions, the simple BGK penalization designed for the one-scale collision [10] cannot capture the correct energy-transport limit. This problem was addressed in [13], where a thresholded BGK penalization was introduced. Here we propose an alternative based on a splitting approach. It has the advantage of treating the collisions at different scales separately, hence is free of choosing threshold and easier to implement. Formal asymptotic analysis and numerical results validate the effciency and accuracy of the proposed scheme.

KW - Asymptotic-preserving scheme

KW - Energy-transport system

KW - Semiconductor boltzmann equation

KW - Splitting method

UR - http://www.scopus.com/inward/record.url?scp=84937425741&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937425741&partnerID=8YFLogxK

U2 - 10.3934/krm.2015.8.707

DO - 10.3934/krm.2015.8.707

M3 - Article

AN - SCOPUS:84937425741

VL - 8

SP - 707

EP - 723

JO - Kinetic and Related Models

JF - Kinetic and Related Models

SN - 1937-5093

IS - 4

ER -