Numerical analysis of the solutions for 1d compressible viscous micropolar fluid flow with different boundary conditions
Numerical analysis of the solutions for 1d compressible viscous micropolar fluid flow with different boundary conditions
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不同边界条件下一维可压缩粘性微极性流体流动解的数值分析
DOI：
10.1016/j.matcom.2016.03.001
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发表时间：
2016
影响因子：
4.6
通讯作者：
N. Mujakovic
中科院分区：
文献类型：
--
作者：
N. Črnjarić;N. Mujakovic
本文的目的是研究一维微极可压缩粘性导热流体流动模型的数值解，该模型在物理意义上是完全多变的。数学模型由四个偏微分方程组成，从欧拉变换到拉格朗日描述，并与不同的边界条件相关联。利用有限差分格式和Faedo-Galerkin方法对问题的结果进行了不同的数值模拟。分析了两种数值格式的性质，并在所选算例上对数值结果进行了比较。对速度和微旋转的均匀边界条件和非均匀边界条件下的数值结果进行了比较，结果表明两种方法具有很好的一致性。然而，所使用的有限差分法的优点在于非齐次边界条件的简单实现，并在近似的自由边界问题上的Faedo-Galerkin方法是不适用的可能性。
The intention of this work is to concern the numerical solutions to the model of the nonstationary 1d micropolar compressible viscous and heat conducting fluid flow that is in the thermodynamical sense perfect and polytropic. The mathematical model consists of four partial differential equations, transformed from the Eulerian to the Lagrangian description, and which are associated with different boundary conditions. By using the finite difference scheme and the Faedo–Galerkin method we make different numerical simulations to the results of our problems. The properties of both numerical schemes are analyzed and numerical results are compared on the chosen test examples. The comparison of the numerical results on problems that have the homogeneous or the non-homogeneous boundary conditions for velocity and microrotation show good agreement of both approaches. However, the advantage of the used finite difference method over the Faedo–Galerkin method lies in the simple implementation of the non-homogeneous boundary conditions and in the possibility of approximation of the free boundary problem on which the Faedo–Galerkin method is not applicable.