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Volume 12, Issue 1
Convergent Finite Difference Scheme for 1D Flow of Compressible Micropolar Fluid

Nermina Mujaković & Nelida Črnjarić-Žic

Int. J. Numer. Anal. Mod., 12 (2015), pp. 94-124.

Published online: 2015-12

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  • Abstract

In this paper we define a finite difference method for the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation and heat flux are proposed. The sequence of approximate solutions for our problem is constructed by using the defined finite difference approximate equations system. We investigate the properties of these approximate solutions and establish their convergence to the strong solution of our problem globally in time, which is the main results of the paper. A numerical experiment is performed by solving the defined approximate ordinary differential equations system using strong-stability preserving (SSP) Runge-Kutta scheme for time discretization.

  • Keywords

micropolar fluid flow, initial-boundary value problem, 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-12-94, author = {Mujaković , Nermina and Črnjarić-Žic , Nelida}, title = {Convergent Finite Difference Scheme for 1D Flow of Compressible Micropolar Fluid}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {1}, pages = {94--124}, abstract = {

In this paper we define a finite difference method for the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation and heat flux are proposed. The sequence of approximate solutions for our problem is constructed by using the defined finite difference approximate equations system. We investigate the properties of these approximate solutions and establish their convergence to the strong solution of our problem globally in time, which is the main results of the paper. A numerical experiment is performed by solving the defined approximate ordinary differential equations system using strong-stability preserving (SSP) Runge-Kutta scheme for time discretization.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/480.html} }
TY - JOUR T1 - Convergent Finite Difference Scheme for 1D Flow of Compressible Micropolar Fluid AU - Mujaković , Nermina AU - Črnjarić-Žic , Nelida JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 94 EP - 124 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/480.html KW - micropolar fluid flow, initial-boundary value problem, finite difference approximations, strong and weak convergence. AB -

In this paper we define a finite difference method for the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation and heat flux are proposed. The sequence of approximate solutions for our problem is constructed by using the defined finite difference approximate equations system. We investigate the properties of these approximate solutions and establish their convergence to the strong solution of our problem globally in time, which is the main results of the paper. A numerical experiment is performed by solving the defined approximate ordinary differential equations system using strong-stability preserving (SSP) Runge-Kutta scheme for time discretization.

Mujaković , Nermina and Črnjarić-Žic , Nelida. (2015). Convergent Finite Difference Scheme for 1D Flow of Compressible Micropolar Fluid. International Journal of Numerical Analysis and Modeling. 12 (1). 94-124. doi:
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