Sparse Data Structures for Efficient State-to-State Kinetic Simulations
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arXiv
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| Format: | Preprint |
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2024
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| author | Gouasmi, Ayoub Murman, Scott |
| author_facet | Gouasmi, Ayoub Murman, Scott |
| contents | Higher-fidelity entry simulations can be enabled by integrating finer thermo-chemistry models into compressible flow physics. One such class of models are State-to-State (StS) kinetics, which explicitly track species populations among quantum energy levels. StS models can represent thermo-chemical non-equilibrium effects that are hardly captured by standard multi-temperature models. However, the associated increase in computational cost is dramatic. For implicit solution techniques that rely on standard block-sparse representations of the Jacobian, both the spatial complexity and the temporal complexity grow quadratically with respect to the number of quantum levels represented. We introduce a more efficient way to represent the Jacobian arising in first-order implicit simulations for compressible flow physics coupled with StS models. The key idea is to recognize that the density of local blocks of the Jacobian comes from rank-one updates that can be managed separately. This leads to a new Jacobian structure, consisting of a fully-sparse matrix and block-wise rank-one updates, whose overall complexity grows linearly with the number of quantum levels. This structure also brings forth a potentially faster variation of the block-Jacobi preconditioning algorithm by leveraging the Sherman-Morrison-Woodbury inversion formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Data Structures for Efficient State-to-State Kinetic Simulations Gouasmi, Ayoub Murman, Scott Computational Physics Mathematical Physics Higher-fidelity entry simulations can be enabled by integrating finer thermo-chemistry models into compressible flow physics. One such class of models are State-to-State (StS) kinetics, which explicitly track species populations among quantum energy levels. StS models can represent thermo-chemical non-equilibrium effects that are hardly captured by standard multi-temperature models. However, the associated increase in computational cost is dramatic. For implicit solution techniques that rely on standard block-sparse representations of the Jacobian, both the spatial complexity and the temporal complexity grow quadratically with respect to the number of quantum levels represented. We introduce a more efficient way to represent the Jacobian arising in first-order implicit simulations for compressible flow physics coupled with StS models. The key idea is to recognize that the density of local blocks of the Jacobian comes from rank-one updates that can be managed separately. This leads to a new Jacobian structure, consisting of a fully-sparse matrix and block-wise rank-one updates, whose overall complexity grows linearly with the number of quantum levels. This structure also brings forth a potentially faster variation of the block-Jacobi preconditioning algorithm by leveraging the Sherman-Morrison-Woodbury inversion formula. |
| title | Sparse Data Structures for Efficient State-to-State Kinetic Simulations |
| topic | Computational Physics Mathematical Physics |
| url | https://arxiv.org/abs/2403.09198 |