Analysis of Carlemann Linearization of Lattice Boltzmann

W. Itani, S. Succi · 2021 · arXiv（正式版见 Commun. Comput. Phys.）

| 编号 QC039 | 主题 量子格子玻尔兹曼 | 链接 arXiv:2111.11327 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

We explore the Carlemann linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible fluid with the Bhatnagar Gross and Krook equilibrium function. Under this assumption, the error in the velocities is proportional to the square of the Mach number. Then, we showcase the Carlemann linearization technique for the system under study. We compute an upper bound to the number of variables as a function of the order of the Carlemann linearization. We study both collision and streaming steps of the lattice Boltzmann formulation under Carlemann linearization. We analytically show why linearizing the collision step sacrifices the exactness of streaming in lattice Boltzmann, while also contributing to the blow up in the number of Carlemann variables in the classical algorithm. The error arising from Carlemann linearization has been shown analytically and numerically to improve exponentially with the Carlemann linearization order. This bodes well for the development of a corresponding quantum computing algorithm based on the Lattice Boltzmann equation.

本站词条在引用该文献时，会以 wikilink（sources/QC039）链接到本页；右侧「反向链接」面板自动列出所有引用它的词条。