A coupled particle-continuum model: well-posedness and the limit of zero radius
A coupled particle-continuum model: well-posedness and the limit of zero radius
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耦合粒子连续体模型：适定性和零半径极限
DOI：
10.1098/rspa.2003.1207
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
James C. Robinson
中科院分区：
文献类型：
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作者：
James C. Robinson
本文讨论了一个简化的燃烧模型，该模型只考虑了燃料颗粒和环境气体之间的动量交换。即使在没有粒子的情况下，也没有三维的严格数学结果，所以我们的注意力仅限于二维情况。将粒子视为点将导致数学问题，而适当的正则化可以绕过这些问题。本文的后半部分研究了当正则化参数在适当的标度下趋于零时模型的行为，表明在极限情况下得到了标准的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。
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.
DOI：
10.1007/978-1-4684-0313-8
发表时间：
1993-09
期刊：
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影响因子：
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作者：
R. Temam
通讯作者：
R. Temam