2015
DOI: 10.17586/2220-8054-2015-6-1-140-145
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On the Stokes flow computation algorithm based on woodbury formula

Abstract: The Stokes approximation is used for the description of flow in nanostructures. An algorithm for Stokes flow computation in cases when there is great variation in the viscosity over a small spatial region is described. This method allows us to overcome computational difficulties of the finite-difference method. The background of the approach is using the Woodbury formula -a discrete analog of the Krein resolvent formula. The particular example of a rectangular domain is considered in detail. The inversion of t… Show more

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Cited by 8 publications
(5 citation statements)
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“…Once the (virtual) copy of the semisimple Lie algebra Gal ℓ (p, q) is found, explicit expression for the Casimir operators can be immediately deduced, in its unsymmetrized analytic form, by means of the well known trace methods (see e.g. [25,26,33,34,35,36,37]). To this extent, let {d, h, c, e i,j , p n,k } be the coordinates in Gal ℓ (p, q) * and let d, h, c, e i,j , p n,k denote the analytical counterpart of the operators in (20).…”
Section: Explicit Formulae For the Casimir Operators Of Gal ℓ (P Q)mentioning
confidence: 99%
“…Once the (virtual) copy of the semisimple Lie algebra Gal ℓ (p, q) is found, explicit expression for the Casimir operators can be immediately deduced, in its unsymmetrized analytic form, by means of the well known trace methods (see e.g. [25,26,33,34,35,36,37]). To this extent, let {d, h, c, e i,j , p n,k } be the coordinates in Gal ℓ (p, q) * and let d, h, c, e i,j , p n,k denote the analytical counterpart of the operators in (20).…”
Section: Explicit Formulae For the Casimir Operators Of Gal ℓ (P Q)mentioning
confidence: 99%
“…A number of benchmark papers have been published over the years, providing test cases to validate new codes. Such comparisons have been published for thermal convection in 2-D (Blankenbach et al, 1989;, 3-D (Busse et al, 1993), 3-D spherical geometry (Stemmer et al, 2006), for thermo-chemical convection (van Keken et al, 1997;Tackley and King, 2003), for the Stokes flow over cavity (Driesen et al, 1998;Popov and Makeev, 2014), for the Stokes flow with variable viscosity , for the Stokes flow with high contrast inclusions (Lobanov et al, 2014;Popov et al, 2015), for viscoplastic thermal convection (Tosi et al, 2015). Analytical benchmark solutions of Stokes equations in cylindrical coordinate system derived in Makeev et al (2015).…”
Section: Introductionmentioning
confidence: 99%
“…Другим способом про-верки является сравнение результата работы алгоритма с эталонными аналитическими решениями неко-торой тестовой задачи. В ряде работ рассматриваются такие решения для декартовой системы координат [5][6][7][8][9][10]. Значительно меньше внимания уделялось эталонным решениям в криволинейных системах коор-динат [11,12], в то время как с вычислительной точки зрения такие случаи являются наиболее сложными.…”
Section: Introductionunclassified