Authors:
Darkhan Akhmed-Zaki
1
;
Nargozy Danaev
1
and
Farida Amenova
2
Affiliations:
1
al-Farabi Kazakh National University, Kazakhstan
;
2
D.Serikbaev East Kazakhstan State Technical University, Kazakhstan
Keyword(s):
Two-dimensional System of the Navier-stokes Equations for an Incompressible Fluid, Linear Stokes Differential Problem, Method of a Priori Estimates, Stability, Convergence, Iterative Algorithm.
Related
Ontology
Subjects/Areas/Topics:
Complex Systems Modeling and Simulation
;
Dynamical Systems Models and Methods
;
Fluid Dynamics
;
Formal Methods
;
Non-Linear Systems
;
Simulation and Modeling
Abstract:
In this paper, mathematical aspects of stability, convergence and numerical implementation of two-dimensional
differential problem for incompressible fluid equations in “stream function, vorticity” variables
defined on a symmetrical template of finite-difference grid studied by method of a priori estimates are considered.
Approximate boundary conditions for the vorticity are chosen in the form of Woods formula. In case
of a linear Stokes problem, it is shown that the numerical solution of the difference problem converges to the
solution of the differential problem with second order accuracy and two algorithms of numerical implementation,
for which the rates of convergence obtained, are considered. In the case of non-linear Navier-Stokes
equations, estimates of the convergence of a solution of the difference problem to the solution of the differential
problem, as well as estimation of the convergence of a considered iterative algorithm with the assumption
that the condition i
s equivalent to the condition of uniqueness of nonlinear difference problem are obtained.
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