Thermodynamically consistent modeling for complex fluids and mathematical analysis
Thermodynamically consistent modeling for complex fluids and mathematical analysis
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复杂流体的热力学一致建模和数学分析
DOI：
10.1142/s0218202521500421
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发表时间：
2021
影响因子：
3.5
通讯作者：
Kawashima Shuichi
中科院分区：
文献类型：
--
作者：
Suzuki Yukihito;Ohnawa Masashi;Mori Naofumi;Kawashima Shuichi
本文的目的是以热力学一致的方式导出复杂流体的控制方程，从而保证能量守恒和熵的增加。该模型是一个关于密度、速度、能量(或相当于温度)和构象张量的一阶偏微分方程组。本文还导出了一个正压模式。在一维情形下，我们将正压模型表示为双曲平衡律的形式，并证明了它满足稳定性条件。从而证明了平衡态附近解的整体存在性，并得到了收敛速度。
The goal of this paper is to derive governing equations for complex fluids in a thermodynamically consistent way so that the conservation of energy and the increase of entropy is guaranteed. The model is a system of first-order partial differential equations on density, velocity, energy (or equivalently temperature), and conformation tensor. A barotropic model is also derived. In the one-dimensional case, we express the barotropic model in the form of hyperbolic balance laws, and show that it satisfies the stability condition. Consequently, the global existence of solutions around equilibrium states is proved and the convergence rates is obtained.