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
KW - spherical symmetry
KW - finite difference approximations
KW - 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 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.