Bekezhanova Victoria B, Goncharova Olga N
Department of Differential Equations of Mechanics, Institute of Computational Modeling SB RAS, Krasnoyarsk, Russia.
World-class Research Center 'Advanced Digital Technologies', Tyumen State University, Tyumen, Russia.
Philos Trans A Math Phys Eng Sci. 2023 Apr 17;381(2245):20220078. doi: 10.1098/rsta.2022.0078. Epub 2023 Feb 27.
The right choice of the appropriate mathematical model is crucial for evaluating the physical plausibility of modelling results. The issue of the correct application of the classical Boussinesq approximation for studying the heat and mass transfer in fluidic systems with a deformable boundary is a subject of scientific discussions despite the good agreement of numerous theoretical and numerical results obtained within the convection models based on the Oberbeck-Boussinesq equations with the data of physical experiments and observations. A comparative analysis of the results of numerical simulations in the framework of two-sided models based on the Navier-Stokes equations, and their Boussinesq approximation, is performed in the context of a convection problem in a locally heated two-phase system with a deformable interface. It is demonstrated that the application of the standard Boussinesq approximation allows one to give a consistent description of the effect of interface deformations on combined buoyant-thermocapillary driven fluid motions. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.
选择合适的数学模型对于评估建模结果的物理合理性至关重要。尽管基于奥伯贝克 - 布辛涅斯克方程的对流模型所获得的众多理论和数值结果与物理实验及观测数据吻合良好，但在研究具有可变形边界的流体系统中的传热传质时，经典布辛涅斯克近似的正确应用问题仍是科学讨论的主题。在具有可变形界面的局部加热两相系统中的对流问题背景下，对基于纳维 - 斯托克斯方程及其布辛涅斯克近似的双边模型框架内的数值模拟结果进行了比较分析。结果表明，应用标准布辛涅斯克近似能够对界面变形对浮力 - 热毛细驱动的流体运动组合的影响给出连贯的描述。本文是“扩展系统图案形成和非线性动力学的新趋势”主题系列的一部分。
