05.13.18 (Mathematical modeling, numerical methods, and the program systems)
Birth date:
08.03.1972
E-mail:
, , ,
Keywords:
stiff systems, chemical reactions, Navier–Stoks equations, numerical methods, mathematical methods.
Subject:
Ph.D. thesis is devoted to simulating of viscous chemical-reacting flows through channel with variable cross section and smooth curved wall. Such problem is important for many scientific and applied purposes, such as developing efficient chemical reactors, turbines, nozzles, estimating concentrations of pollutants in the environment and so on. Numerical investigations of 2D and 3D partial differential equations while taking into account tens different chemical species and hundreds chemical reactions is very hard and labor-consuming computation problem. New effective numerical method for simulation such problems was constructed by E. Alshina. This method is based on new quasi-one-dimensional model for smooth channel and stiff method of lines for numerical solving PDE system. Proposed method gives possibility to compute non-stationary viscous flows taking into account a great number of species and detail mechanism of chemical reactions. It is most important for investigation after burning and estimating harmful pollutants. Usually used global chemical reaction mechanism does not allow such analyses. Stiff method of lines is an effective for calculation stiff system and suitable to simulation of chemical reaction. Recent investigations are devoted to construction numerical methods for boundary value problems in unlimited areas. Quasi-uniform grid with a finite number of knots covers unlimited area. These grids allow taking into account boundary conditions on infinity correctly. At first the new numerical method for calculation of spectra of linear differential operators was offered. The comparison of some iterative methods on a convergence velocity and stability for initial data is carried out. Then initial-boundary value problems for PDE of composite type describe waves processes in mediums with anisotropic dispersion was investigated. Numerical method for calculation such problems in unlimited area was constructed in 2001. The new method was successfully tested on some initial-boundary value problems for PDE of composite type including non-linear PDE.
Biography
Graduated from Faculty of Physics of M. V. Lomonosov Moscow State University (MSU) in 1995 (department of mathematics). Ph.D. thesis was defended in 1995. A list of my works contains 15 titles.
Main publications:
E. A. Alshina, N. N. Kalitkin. Vychislenie spektrov lineinykh differentsialnykh operatorov // DAN, 2001, t. 380, # 4, s. 443–447.
E. A. Alshina. O kvaziodnomernoi zadache vnutrennikh vyazkikh techenii // Matematicheskoe modelirovanie, 1997, t. 9, # 12, s. 57–63.
E. A. Alshina, N. N. Kalitkin, I. A. Sokolova. Kvaziodnomernyi raschet nestatsionarnykh techenii v dozvukovom sople // Matematicheskoe modelirovanie, 1998, t. 10, # 5, s. 109–118.
E. A. Alshina, N. N. Kalitkin, B. V. Rogov, I. A. Sokolova. O tochnosti kvaziodnomernoi modeli gladkogo kanala // Matematicheskoe modelirovanie, 2001, t. 13, # 10, s. 121–124.
A. B. Alshin, E. A. Alshina. Chislennoe reshenie nachalno-kraevykh zadach dlya uravnenii sostavnogo tipa v neogranichennykh oblastyakh // ZhVMiMF.
A. B. Alshin, E. A. Alshina, “About one new two-stages Rosenbrock scheme for differential-algebraic systems”, Matem. Mod., 23:3 (2011), 139–160; Math. Models Comput. Simul., 3:5 (2011), 604–618
A. B. Alshin, E. A. Alshina, A. G. Limonov, “Automatic order conditions symbolic derivation for two-stage complex Rosenbrock scheme”, Matem. Mod., 21:12 (2009), 76–88; Math. Models Comput. Simul., 2:4 (2010), 493–503
3.
A. B. Alshin, E. A. Alshina, A. G. Limonov, “Two-stage complex Rosenbrock schemes for stiff systems”, Zh. Vychisl. Mat. Mat. Fiz., 49:2 (2009), 270–287; Comput. Math. Math. Phys., 49:2 (2009), 261–278
E. A. Alshina, E. S. Ivanchenko, N. N. Kalitkin, V. F. Tishkin, “High-precision invariant on rotation parameterization of curves”, Matem. Mod., 20:1 (2008), 16–28; Math. Models Comput. Simul., 1:1 (2009), 11–20
5.
E. A. Alshina, E. M. Zaks, N. N. Kalitkin, “Optimal first- to sixth-order accurate Runge–Kutta schemes”, Zh. Vychisl. Mat. Mat. Fiz., 48:3 (2008), 418–429; Comput. Math. Math. Phys., 48:3 (2008), 395–405
A. B. Alshin, E. A. Alshina, N. N. Kalitkin, A. B. Koryagina, “Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1392–1414; Comput. Math. Math. Phys., 46:8 (2006), 1320–1340
E. A. Alshina, N. N. Kalitkin, P. V. Koryakin, “Diagnostics of singularities of exact solutions in computations with error control”, Zh. Vychisl. Mat. Mat. Fiz., 45:10 (2005), 1837–1847; Comput. Math. Math. Phys., 45:10 (2005), 1769–1779
E. A. Alshina, A. A. Boltnev, O. A. Kacher, “Gradient methods with improved convergence rate”, Zh. Vychisl. Mat. Mat. Fiz., 45:3 (2005), 374–382; Comput. Math. Math. Phys., 45:3 (2005), 356–365
A. B. Alshin, E. A. Alshina, A. A. Boltnev, O. A. Kacher, P. V. Koryakin, “The numerical solution of initial-boundary value problems for the Sobolev type equations on quasi-uniform grids”, Zh. Vychisl. Mat. Mat. Fiz., 44:3 (2004), 493–513; Comput. Math. Math. Phys., 44:3 (2004), 465–484
A. B. Alshin, E. A. Alshina, “Numerical solution to initial-boundary value problem for composite equations in unbounded domain”, Zh. Vychisl. Mat. Mat. Fiz., 42:12 (2002), 1796–1803; Comput. Math. Math. Phys., 42:12 (2002), 1725–1732
E. A. Alshina, N. N. Kalitkin, B. V. Rogov, I. A. Sokolova, “On accuracy of the quasi-one-dimensional model of smooth wall channel”, Matem. Mod., 13:10 (2001), 120–124
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