Volume 13, Issue 5
Convergence of a Finite Difference Scheme for 3D Flow of a Compressible Viscous Micropolar Heat-Conducting Fluid with Spherical Symmetry

N. Mujaković & N. Črnjarić-Žic

Int. J. Numer. Anal. Mod., 13 (2016), pp. 705-738.

Published online: 2016-09

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  • Abstract

We consider the nonstationary 3D flow of a compressible viscous heat-conducting micropolar fluid in the domain to be a subset of $\boldsymbol{R^3}$, bounded with two concentric spheres. In the thermodynamical sense the fluid is perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation, heat flux and spherical symmetry of the initial data are proposed. Due to the assumption of spherical symmetry, the problem can be considered as one-dimensional problem in Lagrangian description on the domain that is a segment. We define the approximate equations system by using the finite difference method and construct the sequence of approximate solutions for our problem. By analyzing the properties of these approximate solutions we prove their convergence to the generalized solution of our problem globally in time and establish the convergence of the defined numerical scheme, which is the main result of the paper. The practical application of the proposed numerical scheme is performed on the chosen test example.

  • Keywords

micropolar fluid flow, spherical symmetry, finite difference approximations, strong and weak convergence.

  • AMS Subject Headings

35Q35, 76M20, 65M06, 76N99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-705, author = {}, title = {Convergence of a Finite Difference Scheme for 3D Flow of a Compressible Viscous Micropolar Heat-Conducting Fluid with Spherical Symmetry}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {5}, pages = {705--738}, abstract = {

We consider the nonstationary 3D flow of a compressible viscous heat-conducting micropolar fluid in the domain to be a subset of $\boldsymbol{R^3}$, bounded with two concentric spheres. In the thermodynamical sense the fluid is perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation, heat flux and spherical symmetry of the initial data are proposed. Due to the assumption of spherical symmetry, the problem can be considered as one-dimensional problem in Lagrangian description on the domain that is a segment. We define the approximate equations system by using the finite difference method and construct the sequence of approximate solutions for our problem. By analyzing the properties of these approximate solutions we prove their convergence to the generalized solution of our problem globally in time and establish the convergence of the defined numerical scheme, which is the main result of the paper. The practical application of the proposed numerical scheme is performed on the chosen test example.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/461.html} }
TY - JOUR T1 - Convergence of a Finite Difference Scheme for 3D Flow of a Compressible Viscous Micropolar Heat-Conducting Fluid with Spherical Symmetry JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 705 EP - 738 PY - 2016 DA - 2016/09 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/461.html KW - micropolar fluid flow, spherical symmetry, finite difference approximations, strong and weak convergence. AB -

We consider the nonstationary 3D flow of a compressible viscous heat-conducting micropolar fluid in the domain to be a subset of $\boldsymbol{R^3}$, bounded with two concentric spheres. In the thermodynamical sense the fluid is perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation, heat flux and spherical symmetry of the initial data are proposed. Due to the assumption of spherical symmetry, the problem can be considered as one-dimensional problem in Lagrangian description on the domain that is a segment. We define the approximate equations system by using the finite difference method and construct the sequence of approximate solutions for our problem. By analyzing the properties of these approximate solutions we prove their convergence to the generalized solution of our problem globally in time and establish the convergence of the defined numerical scheme, which is the main result of the paper. The practical application of the proposed numerical scheme is performed on the chosen test example.

N. Mujaković & N. Črnjarić-Žic. (2019). Convergence of a Finite Difference Scheme for 3D Flow of a Compressible Viscous Micropolar Heat-Conducting Fluid with Spherical Symmetry. International Journal of Numerical Analysis and Modeling. 13 (5). 705-738. doi:
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