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 Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 11, Pages 1998–2016 (Mi zvmmf4968)

Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders

M. B. Soloviev

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia

Abstract: Numerical implementations of a new fast-converging iterative method with boundary condition splitting are constructed for solving the Dirichlet initial-boundary value problem for the nonstationary Stokes system in the gap between two coaxial cylinders. The problem is assumed to be axially symmetric and periodic along the cylinders. The construction is based on finite-difference approximations in time and bilinear finite-element approximations in a cylindrical coordinate system. A numerical study has revealed that the iterative methods constructed have fairly high convergence rates that do not degrade with decreasing viscosity (the error is reduced by approximately 7 times per iteration step). Moreover, the methods are second-order accurate with respect to the mesh size in the max norm for both velocity and pressure.

Key words: nonstationary Stokes problem, iterative methods with boundary condition splitting, second-order accuracy, finite-difference method, finite element method.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:11, 1895–1913

Bibliographic databases:

UDC: 519.634

Citation: M. B. Soloviev, “Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders”, Zh. Vychisl. Mat. Mat. Fiz., 50:11 (2010), 1998–2016; Comput. Math. Math. Phys., 50:11 (2010), 1895–1913

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. B. V. Pal'tsev, M. B. Soloviev, I. I. Chechel', “On the development of iterative methods with boundary condition splitting for solving boundary and initial-boundary value problems for the linearized and nonlinear Navier–Stokes equations”, Comput. Math. Math. Phys., 51:1 (2011), 68–87
2. B. V. Pal'tsev, “To the theory of asymptotically stable second-order accurate two-stage scheme for an inhomogeneous parabolic initial-boundary value problem”, Comput. Math. Math. Phys., 53:4 (2013), 396–430
3. M. B. Solov'ev, “Numerical implementation of an iterative method with boundary condition splitting for solving the nonstationary stokes problem on the basis of an asymptotically stable two-stage difference scheme”, Comput. Math. Math. Phys., 54:12 (2014), 1817–1825
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