An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions
The present paper deals with the development of a numerical scheme for the solution of two-dimensional Boltzmann transport equation (BTE) under electronic nonequilibrium conditions. A two-dimensional explicit modal discontinuous Galerkin (DG) method with uniform meshes is developed for solving the B...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/156108 |
| _version_ | 1824453650053857280 |
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| author | Singh, Satyvir Battiato, Marco |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Singh, Satyvir Battiato, Marco |
| author_sort | Singh, Satyvir |
| collection | NTU |
| description | The present paper deals with the development of a numerical scheme for the solution of two-dimensional Boltzmann transport equation (BTE) under electronic nonequilibrium conditions. A two-dimensional explicit modal discontinuous Galerkin (DG) method with uniform meshes is developed for solving the BTE in conjunction with the relaxation time approximation. The spatial discretization is carried out using a high-order DG method, where the polynomial solutions are represented using scaled Legendre basis functions. A third-order explicit SSP-RK scheme is applied for temporal discretization to the resulting semi-discrete ordinary differential equation. The analytic steady state solution of BTE at low electromagnetic field is considered as the validation study. The numerical scheme is applied to the description of electron transport in non-linear dynamic conductivity based on static electric field. The electrical and Hall conductivities with nonequilibrium conditions is estimated for the BTE solution in presence of the electromagnetic field. These transport coefficients are also examined with the dependence of temperature and chemical potential. It is observed that the electrical and Hall conductivity decreases in the presence of a magnetic field. Numerical results demonstrate the potential advantages of the high-order scheme in treating ultrafast nonequilibrium dynamics. |
| first_indexed | 2025-02-19T03:09:47Z |
| format | Journal Article |
| id | ntu-10356/156108 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:09:47Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1561082022-04-22T00:51:37Z An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions Singh, Satyvir Battiato, Marco School of Physical and Mathematical Sciences Science::Physics::Nuclear and particle physics Discontinuous Galerkin Method Boltzmann Transport Equation The present paper deals with the development of a numerical scheme for the solution of two-dimensional Boltzmann transport equation (BTE) under electronic nonequilibrium conditions. A two-dimensional explicit modal discontinuous Galerkin (DG) method with uniform meshes is developed for solving the BTE in conjunction with the relaxation time approximation. The spatial discretization is carried out using a high-order DG method, where the polynomial solutions are represented using scaled Legendre basis functions. A third-order explicit SSP-RK scheme is applied for temporal discretization to the resulting semi-discrete ordinary differential equation. The analytic steady state solution of BTE at low electromagnetic field is considered as the validation study. The numerical scheme is applied to the description of electron transport in non-linear dynamic conductivity based on static electric field. The electrical and Hall conductivities with nonequilibrium conditions is estimated for the BTE solution in presence of the electromagnetic field. These transport coefficients are also examined with the dependence of temperature and chemical potential. It is observed that the electrical and Hall conductivity decreases in the presence of a magnetic field. Numerical results demonstrate the potential advantages of the high-order scheme in treating ultrafast nonequilibrium dynamics. Nanyang Technological University This work was supported by the Nanyang Technological University Singapore, through the NAP-SUG grant. 2022-04-22T00:51:36Z 2022-04-22T00:51:36Z 2021 Journal Article Singh, S. & Battiato, M. (2021). An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions. Computers and Fluids, 224, 104972-. https://dx.doi.org/10.1016/j.compfluid.2021.104972 0045-7930 https://hdl.handle.net/10356/156108 10.1016/j.compfluid.2021.104972 2-s2.0-85105695724 224 104972 en NAP-SUG-M408074 Computers and Fluids © 2021 Elsevier Ltd. All rights reserved. |
| spellingShingle | Science::Physics::Nuclear and particle physics Discontinuous Galerkin Method Boltzmann Transport Equation Singh, Satyvir Battiato, Marco An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions |
| title | An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions |
| title_full | An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions |
| title_fullStr | An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions |
| title_full_unstemmed | An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions |
| title_short | An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions |
| title_sort | explicit modal discontinuous galerkin method for boltzmann transport equation under electronic nonequilibrium conditions |
| topic | Science::Physics::Nuclear and particle physics Discontinuous Galerkin Method Boltzmann Transport Equation |
| url | https://hdl.handle.net/10356/156108 |
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