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Article information
2018 , Volume 23, ¹ 2, p.102-116
Rukavishnikov A.V.
Stabilized numerical method for solving the Oseen type problem with a singularity
Purpose. To construct modified approximation approach using the finite element method and to perform numerical analysis for a two dimensional problem on the flow of a viscous inhomogeneous fluids - the Oseen type problem, that is obtained by sampling in time and linearizing the incompressible Navier-Stokes equations. To consider the convection dominated flow case. Methodology. Based on the domain decomposition method with a smooth curvilinear boundary between subdomains, a stabilization nonconformal finite element method is constructed that satisfies the inf-sup-stability condition. To solve the resulting system of linear algebraic equations, an iterative process is considered that uses the decomposition of the vector in the Krylov subspace with minimal inviscidity, with a block preconditioning of the matrix. Findings. The results of the numerical experiments demonstrate the robustness of the considered method for different (even small) discontinuous values of viscosity. The differences between finite element and exact solutions for the velocity field and pressure in the norms of the grid spaces decrease as 𝒪( h ) for each curvilinear interface, that agrees with the theoretical estimate which is proved by the author. Originality/value. Using the stabilized finite element method is often good and better then the classical finite element method for convection dominated flows with discontinuous viscosity and density.
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Keywords: domain decomposition method, Oseen type problem, stabilized finite element method, discontinuous coefficients
doi: 10.25743/ICT.2018.23.12803
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 References:
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Bibliography link:
Rukavishnikov A.V. Stabilized numerical method for solving the Oseen type problem with a singularity // Computational technologies. 2018. V. 23. ¹ 2. P. 102-116
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