Adjoint DSMC Method for Spatially Inhomogeneous Boltzmann Equation with General Boundary Conditions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908905523642368 |
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| author | Caflisch, Russel Yang, Yunan |
| author_facet | Caflisch, Russel Yang, Yunan |
| contents | This manuscript derives adjoint equations for the numerical solution of the spatially inhomogeneous Boltzmann equation using Direct Simulation Monte Carlo (DSMC). The formulation accounts for spatial transport and a range of boundary conditions, including periodic boundaries, specular reflection, thermal reflection, and prescribed inflow. Numerical experiments are presented to validate the resulting adjoint system. These adjoint formulations are intended for use in gradient-based optimization, sensitivity analysis, and design problems involving rarefied gas dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adjoint DSMC Method for Spatially Inhomogeneous Boltzmann Equation with General Boundary Conditions Caflisch, Russel Yang, Yunan Numerical Analysis Optimization and Control 76P05, 82C80, 65C05, 65K10, 82B40, 65M32 This manuscript derives adjoint equations for the numerical solution of the spatially inhomogeneous Boltzmann equation using Direct Simulation Monte Carlo (DSMC). The formulation accounts for spatial transport and a range of boundary conditions, including periodic boundaries, specular reflection, thermal reflection, and prescribed inflow. Numerical experiments are presented to validate the resulting adjoint system. These adjoint formulations are intended for use in gradient-based optimization, sensitivity analysis, and design problems involving rarefied gas dynamics. |
| title | Adjoint DSMC Method for Spatially Inhomogeneous Boltzmann Equation with General Boundary Conditions |
| topic | Numerical Analysis Optimization and Control 76P05, 82C80, 65C05, 65K10, 82B40, 65M32 |
| url | https://arxiv.org/abs/2603.20946 |