
This article is cited in 5 scientific papers (total in 5 papers)
On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers
B. V. Pal'tsev^{}, I. I. Chechel'^{} ^{} Dorodnicyn Computing Center, Russian Academy of Sciences,
ul. Vavilova 40, Moscow, 119991, Russia
Abstract:
The convergence rate of a fastconverging secondorder accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For $R/r$ exceeding about 30, where $r$ and $R$ are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large $R/r$) than the convergence rate of its differential version. For this
reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finiteelement implementation of this modification is built. Numerical experiments have
revealed that this modification has the same convergence rate as its differential counterpart for $R/r$ of up to $5\times10^3$. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from $R/r\sim30$ and is considerably more efficient for large values of $R/r$. It is also established that the convergence rates of both methods depend little on the stretching coefficient $\eta$ of circularly rectangular mesh cells in a range of $\eta$ that is well sufficient for effective use of the multigrid method for arbitrary values of $R/r$ smaller than $\sim 5\times10^3$.
Key words:
stationary Stokes system, spherical gaps, iterative methods with splitting of boundary conditions, secondorder accurate finiteelement implementations in the axisymmetric case, convergence rates, multigrid method.
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Computational Mathematics and Mathematical Physics, 2006, 46:5, 820–847
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UDC:
519.634 Received: 02.12.2005
Citation:
B. V. Pal'tsev, I. I. Chechel', “On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 858–886; Comput. Math. Math. Phys., 46:5 (2006), 820–847
Citation in format AMSBIB
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M. K. Kerimov, “Boris Vasil'evich Pal'tsev (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 50:7 (2010), 1113–1119

B. V. Pal'tsev, M. B. Soloviev, I. I. Chechel', “On the development of iterative methods with boundary condition splitting for solving boundary and
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B. V. Pal'tsev, M. B. Solov'ev, I. I. Chechel', “Numerical study of spherical Couette flows for certain zenithangledependent rotations of boundary spheres at low Reynolds numbers”, Comput. Math. Math. Phys., 56:6 (2012), 940–975

B. V. Pal'tsev, M. B. Solov'ev, I. I. Chechel', “On the structure of steady axisymmetric NavierStokes flows with a stream function having multiple local extrema in its definitesign domains”, Comput. Math. Math. Phys., 53:11 (2013), 1696–1719

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