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 -