耦合粒子-连续介质模型:适定性和零半径极限

James C. Robinson
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引用次数: 6

摘要

本文讨论了一种简化的燃烧模型,该模型只考虑了燃料颗粒与周围气体之间的动量交换。即使在没有粒子的情况下,也没有严格的三维数学结果,所以我们的注意力仅限于二维的情况。将粒子视为点会导致数学问题,而这些问题可以通过适当的正则化来规避。本文的后半部分研究了该正则化参数在适当的尺度下趋于零时模型的行为,表明在极限下得到标准的Navier-Stokes方程,并且对于数值(Galerkin)近似,粒子的路径将接近流体流线。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A coupled particle-continuum model: well-posedness and the limit of zero radius
This paper treats a simplified model of combustion that takes into account only the exchange of momentum between the fuel particles and ambient gas. Even in the absence of particles there are no rigorous mathematical results available in three dimensions, so our attention is restricted to the two-dimensional case. Treating the particles as points leads to mathematical problems that are circumvented by an appropriate regularization. The latter sections of the paper study the behaviour of the model as this regularization parameter tends to zero under some appropriate scalings, showing that in the limit the standard Navier-Stokes equations are obtained, and that for numerical (Galerkin) approximations the paths of the particles will approach fluid streamlines.
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期刊介绍: Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.
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