Explicit modal discontinuous galerkin approximations for three-dimensional Electronic boltzmann transport equation

• Main Authors: Singh, Satyvir, Battiato, Marco
• Other Authors: School of Physical and Mathematical Sciences
• Format: Conference or Workshop Item
• Language: English
• Published: 2022
• Subjects: Science::Physics::Electricity and magnetism; Boltzmann Transport Equation; Algorithms
• Online Access: https://hdl.handle.net/10356/156097; https://www.conftool.com/icosahom2020/index.php?page=browseSessions&form_session=45#paperID195
• Institution: Nanyang Technological University

This study presents the development of an efficient numerical algorithm to simulate the three-dimensional electronic Boltzmann transport equation (BTE) in equilibrium to nonequilibrium regimes, within a single framework. A threedimensional explicit modal discontinuous Galerkin approximation based on hexahedral elements was developed to solve the electronic BTE in conjunction with the relaxation time approximation. The hierarchical basis functions based on orthogonal scaled Legendre polynomials were used, while the Gaussian quadrature rule was adopted for evaluating surface and volume integration. The upwind scheme was used for handling the numerical flux function, while, an explicit third-order accurate SSP-RK scheme was used for temporal discretization. A three-dimensional linear scalar problem was solved to verify the order of accuracy of the numerical scheme. After then, an extensive range of numerical simulations was conducted to investigate the effects of physical parameters on electronic BTE dynamics. The numerical experiments show that the proposed system treats ultrafast dynamics consistently and effectively across a wide range of parameters and regimes.