An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas
We consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-02-01
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| Series: | Results in Applied Mathematics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037419300858 |
| _version_ | 1819017793698267136 |
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| author | Alexander Alekseenko Amy Grandilli Aihua Wood |
| author_facet | Alexander Alekseenko Amy Grandilli Aihua Wood |
| author_sort | Alexander Alekseenko |
| collection | DOAJ |
| description | We consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares problem derived from the Boltzmann equation with full collision integral. Our model performs well for flows obtained by mixing upstream and downstream conditions of normal shock wave with Mach number 3. The model was applied to explore the process of approaching equilibrium in a spatially homogeneous flow of gas. Convergence of solutions with respect to the model parameters is studied. MSC: 76P05, 76M10, 65M60, Keywords: Boltzmann equation, Sparse approximation, Kinetic solutions, Non-continuum gas |
| first_indexed | 2024-12-21T03:09:10Z |
| format | Article |
| id | doaj.art-92167d2b984048e1b0f2c4535c5e36bb |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-12-21T03:09:10Z |
| publishDate | 2020-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-92167d2b984048e1b0f2c4535c5e36bb2022-12-21T19:18:01ZengElsevierResults in Applied Mathematics2590-03742020-02-015An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gasAlexander Alekseenko0Amy Grandilli1Aihua Wood2Department of Mathematics, California State University Northridge, Northridge, CA 91330, USA; Corresponding author.Department of Mathematics, California State University Northridge, Northridge, CA 91330, USADepartment of Mathematics & Statistics, Air Force Institute of Technology, WPAFB, OH 45433, USAWe consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares problem derived from the Boltzmann equation with full collision integral. Our model performs well for flows obtained by mixing upstream and downstream conditions of normal shock wave with Mach number 3. The model was applied to explore the process of approaching equilibrium in a spatially homogeneous flow of gas. Convergence of solutions with respect to the model parameters is studied. MSC: 76P05, 76M10, 65M60, Keywords: Boltzmann equation, Sparse approximation, Kinetic solutions, Non-continuum gashttp://www.sciencedirect.com/science/article/pii/S2590037419300858 |
| spellingShingle | Alexander Alekseenko Amy Grandilli Aihua Wood An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas Results in Applied Mathematics |
| title | An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas |
| title_full | An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas |
| title_fullStr | An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas |
| title_full_unstemmed | An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas |
| title_short | An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas |
| title_sort | ultra sparse approximation of kinetic solutions to spatially homogeneous flows of non continuum gas |
| url | http://www.sciencedirect.com/science/article/pii/S2590037419300858 |
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