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Erschienen in: Mathematical Models and Computer Simulations 2/2020

01.03.2020

Accounting Method of Filling Cells for the Solution of Hydrodynamics Problems with a Complex Geometry of the Computational Domain

verfasst von: A. I. Sukhinov, A. E. Chistyakov, E. A. Protsenko, V. V. Sidoryakina, S. V. Protsenko

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 2/2020

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Abstract

This article is devoted to the development and application of the filling cells method for the solution of hydrodynamics problems with a complicated geometry of the computational domain, in particular, a liquid domain, to increase the smoothness and accuracy of the finite-difference solution. The spatial-two-dimensional flow problem of a viscous fluid between two coaxial semicylinders and the spatial-three-dimensional problem of wave propagation in the coastal zone demonstrate the possibilities of the proposed method. The rectangular grids are used to solve these problems, taking into account the filling of cells. The approximation of problems are used to split schemes in time for physical processes and the approximation in spatial variables is made using the balance method, taking into account the filling of cells and without it. An analytical solution describing the Taylor-Couette flow is used as the reference to assess the accuracy of the numerical solution of the first problem. The simulation is performed on a a sequence of condensing computational grids with the following dimensions: 11 × 21, 21 × 41, 41 × 81, and 81 × 161 nodes in the case of using the method and without using it. In the case of the direct use of rectangular grids (stepwise approximation of boundaries), the relative error of the calculations reaches 70%; under the same conditions, the use of the proposed method allows us to reduce the error to 6%. It is shown that splitting up the rectangular grid by factors of 2 to 8 in each of the spatial directions does not lead to the same increase in the accuracy of the numerical solutions obtained taking into account the filling of the cells.

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Literatur
3.
Zurück zum Zitat A. V. Nikitina, M. V. Puchkin, I. S. Semenov, A. I. Sukhinov, G. A. Ugolnitskii, A. B. Usov, and A. E. Chistiakov, “Differential-game model for the prevention of kills in shallow water bodies,” Upravl. Bol’sh. Sist. 55, 343–361 (2015). A. V. Nikitina, M. V. Puchkin, I. S. Semenov, A. I. Sukhinov, G. A. Ugolnitskii, A. B. Usov, and A. E. Chistiakov, “Differential-game model for the prevention of kills in shallow water bodies,” Upravl. Bol’sh. Sist. 55, 343–361 (2015).
4.
Zurück zum Zitat A. I. Sukhinov, A. E. Chistyakov, and E. V. Alekseenko, “Numerical realization of the three-dimensional model of hydrodynamics for shallow water basins on a high-performance system,” Math. Models Comput. Simul. 3, 562–574 (2011).MathSciNetCrossRef A. I. Sukhinov, A. E. Chistyakov, and E. V. Alekseenko, “Numerical realization of the three-dimensional model of hydrodynamics for shallow water basins on a high-performance system,” Math. Models Comput. Simul. 3, 562–574 (2011).MathSciNetCrossRef
5.
Zurück zum Zitat A. S. Monin, “Turbulence and microstructure in the ocean,” Phys. Usp. 16, 121–131 (1973).CrossRef A. S. Monin, “Turbulence and microstructure in the ocean,” Phys. Usp. 16, 121–131 (1973).CrossRef
6.
Zurück zum Zitat Yu. I. Shokin, Computational Experiment in the Tsunami Problem, Ed. by Yu. I. Shokin, L. B. Chubarov, An. G. Marchuk, and K. V. Simonov (Nauka, Novosibirsk, 1989) [in Russian]. Yu. I. Shokin, Computational Experiment in the Tsunami Problem, Ed. by Yu. I. Shokin, L. B. Chubarov, An. G. Marchuk, and K. V. Simonov (Nauka, Novosibirsk, 1989) [in Russian].
7.
Zurück zum Zitat B. N. Chetverushkin and M. V. Yakobovskiy, “Numerical algorithms and architecture of HPC systems,” KIAM Preprint No. 52 (Keldysh Inst. Appl. Math., Moscow, 2018). B. N. Chetverushkin and M. V. Yakobovskiy, “Numerical algorithms and architecture of HPC systems,” KIAM Preprint No. 52 (Keldysh Inst. Appl. Math., Moscow, 2018).
8.
Zurück zum Zitat L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987). L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).
9.
Zurück zum Zitat M. M. Krasnov, P. A. Kuchugov, M. E. Ladonkina, and V. F. Tishkin, “Discontinuous Galerkin method on three-dimensional tetrahedral grids: using the operator programming method,” Math. Models Comput. Simul. 9, 529–543 (2017).MathSciNetCrossRef M. M. Krasnov, P. A. Kuchugov, M. E. Ladonkina, and V. F. Tishkin, “Discontinuous Galerkin method on three-dimensional tetrahedral grids: using the operator programming method,” Math. Models Comput. Simul. 9, 529–543 (2017).MathSciNetCrossRef
10.
Zurück zum Zitat O. Yu. Milyukova and V. F. Tishkin, “A multigrid method for a heat equation with discontinuous coefficients with a special choice of grids,” Math. Models Comput. Simul. 8, 118–128 (2016).MathSciNetCrossRef O. Yu. Milyukova and V. F. Tishkin, “A multigrid method for a heat equation with discontinuous coefficients with a special choice of grids,” Math. Models Comput. Simul. 8, 118–128 (2016).MathSciNetCrossRef
11.
Zurück zum Zitat V. A. Gasilov, I. V. Gasilova, L. V. Klochkova, Yu. A. Poveshchenko, and V. F. Tishkin, “Difference schemes based on the support operator method for fluids dynamics problems in a collector containing gas hydrates,” Comput. Math. Math. Phys. 55, 1310–1323 (2015).MathSciNetCrossRef V. A. Gasilov, I. V. Gasilova, L. V. Klochkova, Yu. A. Poveshchenko, and V. F. Tishkin, “Difference schemes based on the support operator method for fluids dynamics problems in a collector containing gas hydrates,” Comput. Math. Math. Phys. 55, 1310–1323 (2015).MathSciNetCrossRef
12.
Zurück zum Zitat O. M. Belotserkovskiy, Turbulence: New Approaches (Nauka, Moscow, 2003) [in Russian]. O. M. Belotserkovskiy, Turbulence: New Approaches (Nauka, Moscow, 2003) [in Russian].
13.
Zurück zum Zitat O. M. Belotserkovskii, V. A. Gushchin, and V. V. Shchennikov, “Use of the splitting method to solve problems of the dynamics of a viscous incompressible fluid USSR,” Comput. Math. Math. Phys. 15, 190–200 (1975).CrossRef O. M. Belotserkovskii, V. A. Gushchin, and V. V. Shchennikov, “Use of the splitting method to solve problems of the dynamics of a viscous incompressible fluid USSR,” Comput. Math. Math. Phys. 15, 190–200 (1975).CrossRef
14.
Zurück zum Zitat O. M. Belotserkovskiy, V. A. Gushchin, and V. N. Kon’shin, “The splitting method for investigating flows of a stratified liquid with a free surface,” USSR Comput. Math. Math. Phys. 27, 181–191 (1987).CrossRef O. M. Belotserkovskiy, V. A. Gushchin, and V. N. Kon’shin, “The splitting method for investigating flows of a stratified liquid with a free surface,” USSR Comput. Math. Math. Phys. 27, 181–191 (1987).CrossRef
15.
Zurück zum Zitat A. I. Sukhinov, A. E. Chistyakov, and N. A. Fomenko, “Methods of construction difference scheme for problems of diffusion=convection-reaction, takes into the degree filling of the control volume,” Izv. YUFU, Tekh. Nauki, No. 4 (141), 87–98 (2013). A. I. Sukhinov, A. E. Chistyakov, and N. A. Fomenko, “Methods of construction difference scheme for problems of diffusion=convection-reaction, takes into the degree filling of the control volume,” Izv. YUFU, Tekh. Nauki, No. 4 (141), 87–98 (2013).
16.
Zurück zum Zitat A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, Basel, 2001). A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, Basel, 2001).
17.
Zurück zum Zitat A. A. Samarskiy and P. N. Vabishchevich, Numerical Methods for Solving Convection-Diffusion Problems (Editorial URSS, Moscow, 1999) [in Russian]. A. A. Samarskiy and P. N. Vabishchevich, Numerical Methods for Solving Convection-Diffusion Problems (Editorial URSS, Moscow, 1999) [in Russian].
18.
Zurück zum Zitat A. A. Samarskiy and E. S. Nikolayev, Methods for Solving Grid Equations (Nauka, Moscow, 1978) [in Russian]. A. A. Samarskiy and E. S. Nikolayev, Methods for Solving Grid Equations (Nauka, Moscow, 1978) [in Russian].
19.
Zurück zum Zitat A. I. Sukhinov and A. E. Chistyakov, “Adaptive modified alternating triangular iterative method for solving grid equations with a NonSelfAdjoint operator,” Math. Models Comput. Simul. 4, 398–409 (2012).MathSciNetCrossRef A. I. Sukhinov and A. E. Chistyakov, “Adaptive modified alternating triangular iterative method for solving grid equations with a NonSelfAdjoint operator,” Math. Models Comput. Simul. 4, 398–409 (2012).MathSciNetCrossRef
20.
Zurück zum Zitat S. V. Vallander, Lectures on Hydroaeromechanics, The Handbook (LGU, Leningrad, 1978) [in Russian]. S. V. Vallander, Lectures on Hydroaeromechanics, The Handbook (LGU, Leningrad, 1978) [in Russian].
21.
Zurück zum Zitat I. S. Menshov and M. A. Kornev, “Free boundary method for numerical solving gas dynamics equations in domains with varying geometry,” Math. Models Comput. Simul. 26, 612–621 (2014).CrossRef I. S. Menshov and M. A. Kornev, “Free boundary method for numerical solving gas dynamics equations in domains with varying geometry,” Math. Models Comput. Simul. 26, 612–621 (2014).CrossRef
22.
Zurück zum Zitat A. E. Lutsky, I. S. Menshov, and Ya. V. Khankhasaeva, “Numerical simulation of the wake influence on the flow around truncated cone,” Math. Models Comput. Simul. 9, 92–100 (2017).MathSciNetCrossRef A. E. Lutsky, I. S. Menshov, and Ya. V. Khankhasaeva, “Numerical simulation of the wake influence on the flow around truncated cone,” Math. Models Comput. Simul. 9, 92–100 (2017).MathSciNetCrossRef
Metadaten
Titel
Accounting Method of Filling Cells for the Solution of Hydrodynamics Problems with a Complex Geometry of the Computational Domain
verfasst von
A. I. Sukhinov
A. E. Chistyakov
E. A. Protsenko
V. V. Sidoryakina
S. V. Protsenko
Publikationsdatum
01.03.2020
Verlag
Pleiades Publishing
Erschienen in
Mathematical Models and Computer Simulations / Ausgabe 2/2020
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI
https://doi.org/10.1134/S2070048220020155

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