Journal "Computational Technologies"

Article information

2022 , Volume 27, № 6, p.70-87

Rukavishnikov A.V.

On the optimal set of parameters for an approximate method for solving stationary nonlinear Navier - Stokes equations with singularity

The purpose of this paper is finding the optimal set of parameters for the constructed approximate method for solving the stationary Navier – Stokes equations. The search for a solution to a nonlinear problem is reduced to a sequence of approximate linear problems using values from previous iterations in the nonlinear convective term. The peculiarity of the problem lies in the fact that the computational domain is a non-convex polygon with a re-entranter part of the domain, where the solution has sufficient smoothness. In this case, the order of convergence of the approximate solution to the exact one is significantly less than for convex regions. The proposed numerical method overcomes these difficulties. It is based on two ideas, namely, the introduction into the variational formulation of problems a weight function to some degree and special basis functions.

In the course of numerical experiments, a set of optimal parameters of the method was determined. The order of convergence of the approximate solution to the exact one of the nonlinear problem is the same for angles more than 𝜋 and significantly greater than those which use classical approaches. Part of the optimal set of free parameters of the proposed method does not depend on the value of the re-entrant angle. The optimal convergence rate is achieved without using a mesh refinement in the vicinity of the singularity point.

[full text]
Keywords: nonlinear Navier - Stokes equations, singularity, finite element method

doi: 10.25743/ICT.2022.27.6.007

Author(s):
Rukavishnikov Alexey Victorovich
PhD. , Associate Professor
Position: Leading research officer
Office: Computing Center of the Far-Eastern Branch Russian Academy of Sciences
Address: 680000, Russia, Khabarovsk, 65, Kim Yu Chen Str.
Phone Office: (4212) 70-43-42
SPIN-code: 7680-1450

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Bibliography link:
Rukavishnikov A.V. On the optimal set of parameters for an approximate method for solving stationary nonlinear Navier - Stokes equations with singularity // Computational technologies. 2022. V. 27. № 6. P. 70-87