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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.20101 |
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| _version_ | 1866913523289817088 |
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| author | Rao, S. V. Raghurama Shrinath, K. S. Ruhi, Ankit Rao, Veeredhi Vasudeva |
| author_facet | Rao, S. V. Raghurama Shrinath, K. S. Ruhi, Ankit Rao, Veeredhi Vasudeva |
| contents | A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic scheme is then introduced for solving a wide variety of nonlinear convection-diffusion equations numerically. Based on this framework, a generalized kinetic Lax-Wendroff scheme is also derived, recovering the classical Lax-Wendroff method as one of the choices. Further, a total variation diminishing version of this kinetic flux difference splitting scheme is presented, combining it with the kinetic Lax-Wendroff scheme using a limiter function. The numerical scheme has been extensively tested and the results for benchmark test cases, for 1D and 2D nonlinear convection and convection-diffusion equations, are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20101 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Flexible Velocity Boltzmann Scheme for Convection-Diffusion Equations Rao, S. V. Raghurama Shrinath, K. S. Ruhi, Ankit Rao, Veeredhi Vasudeva Numerical Analysis A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic scheme is then introduced for solving a wide variety of nonlinear convection-diffusion equations numerically. Based on this framework, a generalized kinetic Lax-Wendroff scheme is also derived, recovering the classical Lax-Wendroff method as one of the choices. Further, a total variation diminishing version of this kinetic flux difference splitting scheme is presented, combining it with the kinetic Lax-Wendroff scheme using a limiter function. The numerical scheme has been extensively tested and the results for benchmark test cases, for 1D and 2D nonlinear convection and convection-diffusion equations, are presented. |
| title | A Flexible Velocity Boltzmann Scheme for Convection-Diffusion Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.20101 |