AN ASYMPTOTIC-PRESERVING SCHEME FOR THE SEMICONDUCTOR BOLTZMANN EQUATION WITH TWO-SCALE COLLISIONS: A SPLITTING APPROACH

作者：Hu, Jingwei; Jin, Shi; Wang, Li^*

来源：Kinetic and Related Models, 2015, 8(4): 707-723.

DOI：10.3934/krm.2015.8.707

• Semiconductor Boltzmann equation
• energy-transport system
• asymptotic-preserving scheme
• splitting method

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 sphtting 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 efficiency and accuracy of the proposed scheme.

• 出版日期2015-12
• 单位上海交通大学