THE ALGORITHM OF MESHFREE METHOD OF RADIAL BASIS FUNCTIONS IN TASKS OF UNDERGROUND HYDROMECHANICS

N. V. Medvid; P. M. Martinyuk

THE ALGORITHM OF MESHFREE METHOD OF RADIAL BASIS FUNCTIONS IN TASKS OF UNDERGROUND HYDROMECHANICS

N. V. Medvid, P. M. Martinyuk

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Abstract

A Mathematical model of filtering consolidation in the body of soil dam with conduit and
washout zone in two-dimensional case is considered. The impact of such technogenic factors as temperature, salt concentration, subsidence of upper boundary and interior points of the dam with time is taken into account. The software to automate the calculation of numerical solution of the boundary problem by radial basis functions has been created, which enables to conduct numerical experiments by varying the input parameters and shape. The influence of the presence of conduit and washout zone on the pressure, temperature and concentration of salts in the dam body at different time intervals is
investigated. A number of numerical experiments is conducted and the analysis of dam accidents is performed.

References

1. Kindler, E. Object-oriented simulation of systems with sophisticated control / E. Kindler,I. Krivy // Intern. J. of General Systems. - 2011. - Vol. 40. - P. 313-343.

2. Korchevskaya, E.A. Sovremennye chislennye metody v ob"ektno-orientirovannom izlozhenii / E.A. Korchevskaya // Nauka - obrazovaniyu, proizvodstvu, ekonomike : materialy XX(67) Regional'noi nauch.-prakt. konf. prepodavatelei, nauch. sotrudnikov i aspirantov, Vitebsk. - Vitebsk : VGU im. P.M. Masherova, 2015. - T. 1. - S. 10-11.

3. Martynyuk, P.N. Reshenie kraevykh zadach dlya sistem kvazilineinykh parabolicheskikh uravnenii setochnymi i bessetochnymi chislennymi metodami / P.N. Martynyuk // Sibirskie elektronnye matematicheskie izvestiya [Elektronnyi resurs]. - 2014. - T. 11. - S. 476-493. - Rezhim dostupa : http://semr.math.nsc.ru/v11/p476-493.pdf. - Data dostupa : 18.05.2016.

4. Liu, G.R. Meshfree methods. Moving beyond the finite element method / G.R. Liu. - CRC Press, 2010. - 792 p.

5. Vlasova, E.A. Priblizhennye metody matematicheskoi fiziki / E.A. Vlasova, V.S. Zarubin, G.N. Kuvyrnin. - M. : Izd-vo MGTU im. N.E. Baumana, 2001. - 700 s.

6. Liu, G.R. An introduction to meshfree methods and their programming / G.R. Liu, Y.T. Gu. - Springer, 2005. - 480 p.

7. Franke, C. Solving partial differential eguations by collocation using radial basis fubction / C. Franke, R. Schaback // Appl. Math. Comp. - 1998. - Vol. 93. - P. 73-82.

8. Franke, C. Convergence order estimates of meshless collocation methods using radial basis functions / C. Franke, R. Schaback // Advances in computational mathematics. - 1998. - Vol. 8(4). - P. 381-399.

9. Kansa, E.J. Multiquadrics - a scattered data approximation scheme with applications to computtional fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations / E.J. Kansa // Comput. Math. Appl. - 1990. - Vol. 19. - P. 147-161.

10. Pang, G. Space-fractional advection-dispersion equations by the Kansa method / G. Pang, W. Chen, Z. Fu // J. of Computational Physics. - 2015. - Vol. 293. - P. 280-296.

11. Mavric, B. Local radial basis function collocation method for linear thermoelasticity in two dimensions / B. Mavric, B. Sarler // Intern. J. Numerical Methods for Heat and Fluid Flow. - 2015. - Vol. 25, no. 6. - P. 148-1510.

12. Uddin, M. On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method / M. Uddin // Applied Mathematical Modelling. - 2014. - Vol. 38. - P. 135-144.

13. Pearson, J.W. A radial basis function method for solving PDE constrained optimization problems / J.W. Pearson // Numerical Algorithms. - 2013. - Vol. 64. - P. 481-506.

14. Tolstykh, A.I. Bessetochnyi metod na osnove radial'nykh bazisnykh funktsii / A.I. Tolstykh, D.A. Shirobokov // Zhurnal vychisl. matem. i matem. fiz. - 2005. - T. 45, № 8. - S. 1498-1505.

15. Biazar, J. Galerkin RBF for integro-differential eguations / J. Biazar, M.A. Asadi // British Journal of Mathematics and Computer Science. - 2015. - Vol. 11(2). - P. 1-9.

16. Anakhaev, K.N. Ob avariyakh i povrezhdeniyakh zemlyanykh plotin s vodovodami: prichiny i sposoby sovershenstvovaniya protivofil'tratsionnoi zashchity / K.N. Anakhaev, K.A. Gegiev, B.Kh. Amshokov // Gidrotekhnicheskoe stroitel'stvo. - 2014. - № 3. - S. 30-36.

17. Vlasyuk, A.P. Fil'tratsionnaya konsolidatsiya trekhfaznykh gruntov s uchetom polzuchesti skeleta i vliyaniya soleperenosa v neizotermicheskom rezhime / A.P. Vlasyuk, P.N. Martynyuk // Matematicheskoe modelirovanie. - 2010. - T. 22, № 4. - S. 32-56.

18. Vlasyuk, A.P. Kontaktnyi razmyv i fil'tratsionnaya konsolidatsiya gruntov v usloviyakh teplosoleperenosa / A.P. Vlasyuk, P.N. Martynyuk // Matematicheskoe modelirovanie. - 2012. - T. 24, № 11. - S. 97-112.

19. Michuta, O.R. Modelirovanie vliyaniya khimicheskoi suffozii na fil'tratsionnuyu konsolidatsiyu zasolennykh gruntov v neizotermicheskikh usloviyakh / O.R. Michuta, A.P. Vlasyuk, P.N. Martynyuk // Matematicheskoe modelirovanie. - 2013. - T. 25, № 2. - S. 3-18.

20. Vlasyuk, A.P. Numerical solution of three-dimensional problems of filtration consolidation with regard for the influence of technogenic factors by the method of radial basis functions / A.P. Vlasyuk, P.M. Martynyuk // J. of Mathematical Sciences. - 2010. - Vol. 171, no. 5. - P. 632-648.

21. Sergienko, I.V. Matematicheskoe modelirovanie i issledovanie protsesov v neodnorodnykh sredakh / I.V. Sergienko, V.V. Skopetskii, V.S. Deineka. - Kiev : Nauk. dumka, 1991. - 432 s.

22. Martynyuk, P.M. Existence and unigueness of a solution of the problem with free boundary in the theory of filtration consolidation of soil with regard for the influence of technogenic factors / P.M. Martynyuk // J. of Mathematical Sciences. - 2015. - Vol. 207, no. 1. - P. 59-73.

23. Martynyuk, P.N. Uzlovoe i konechno-elementnoe pokrytiya dvumernykh oblastei: nekotorye algoritmy i ikh programmnaya realizatsiya / P.N. Martynyuk, Yu.A. Semenchuk // Vestnik Nats. un-ta vodn. khoz-va i prirodopol'zovaniya. Ser. «Tekhnicheskie nauki». - 2010. - Vyp. 4(52). - S. 202-209.

24. Du, Q. Meshfree, probabilistic determination of point sets and support regions for meshless computing / Q. Du, M. Gunzburger, L. Ju // Computer Methods in Applied Mechanics and Engineering. - 2002. - Vol. 191(13-14). - P. 1349-1366.

25. Fornberg, B. Fast generation of 2-D node distributions for mesh-free PDE discretizations / B. Fornberg, N. Flyer // Computersand Mathematics with Applications. - 2015. - Vol. 69(7). - P. 531-544.

26. Lee, C.-F. On convergent numerical algorithms for onsymmetric collocation / C.-F. Lee, L. Ling, R. Schaback // Advances in computational mathematics. - 2009. - Vol. 30(4). - P. 339-354.

27. Ling, L. Stable and convergent unsymmetric meshless collocation methods / L. Ling, R. Schaback // SYAM J. on numerical analysis. - 2008. - Vol. 46(3). - P. 1097-1115.

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Medvid N.V., Martinyuk P.M. THE ALGORITHM OF MESHFREE METHOD OF RADIAL BASIS FUNCTIONS IN TASKS OF UNDERGROUND HYDROMECHANICS. Informatics. 2016;(4):20-32. (In Russ.)

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THE ALGORITHM OF MESHFREE METHOD OF RADIAL BASIS FUNCTIONS IN TASKS OF UNDERGROUND HYDROMECHANICS

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THE ALGORITHM OF MESHFREE METHOD OF RADIAL BASIS FUNCTIONS IN TASKS OF UNDERGROUND HYDROMECHANICS

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About the Authors

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