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Solving the Transport-Coagulation Problem in a Two-Dimensional Spatial Region

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The article presents a numerical scheme for solving the spatially nonhomogeneous coagulation problem. The problem is solved in a two-dimensional spatial region using unstructured grids. The finite-volume method is used with monotonicity-preserving limiters. The coagulation kernel in the Smoluchowski collision integrals is approximated by a low-rank decomposition, which reduces the machine time requirement. Reflection is reduced by introducing a perfectly matched layer on the spatial boundary.

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References

  1. R. R. Zagidullin, A. P. Smirnov, S. A. Matveev, and E. E. Tyrtyshnikov, “An efficient numerical method for a mathematical model of a transport of coagulating particles,” Moscow Univ. Comput. Math. and Cybern.,41, 179–186 (2017).

    Article  MathSciNet  Google Scholar 

  2. V. B. Betelin and V. A. Galkin, “On the formation of structures in the nonlinear problems of physical kinetics,” Dokl. Math. (2019).

  3. F. Denner and B. G. M. van Wachem, “TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness,” J. Comput. Physics,298, 466–479 (2015).

    Article  MathSciNet  Google Scholar 

  4. M. S. Darwish and F. Moukalled, “TVD schemes for unstructured grids,” Intern. J. Heat and Mass Transfer,46, 599–611 (2003).

    Article  Google Scholar 

  5. A. Syrakos, S. Varchanis, Y. Dimakopoulos, A. Goulas, and J. Tsamopoulos, “A critical analysis of some popular methods for the discretization of the gradient operator in finite volume methods,” Physics of Fluids,29, 127103 (2017).

    Article  Google Scholar 

  6. E. Sozer, C. Brehm, and C. C. Kiris, Gradient Calculation Methods on Arbitrary Polyhedral Meshes for Cell-Centered CFD Solvers, Science and Technology Forum and Exposition: Conference Paper (2014).

  7. S. A. Matveev, E. E. Tyrtyshnikov, A. P. Smirnov, N. V. Brilliantov, “A fast numerical method for solving the Smoluchowski-type kinetic equations of aggregation and fragmentation processes,” Vych. Met. Program.,15, 1–8 (2014).

    Google Scholar 

  8. E. E. Tyrtyshnikov, “Incomplete cross approximation in the mosaic-skeleton methods,” Program.,64, 367–380 (2000).

    MathSciNet  MATH  Google Scholar 

  9. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Physics,114, 185–200 (1994).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    R. R. Zagidullin

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  1. R. R. Zagidullin
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Correspondence to R. R. Zagidullin.

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Translated from Prikladnaya Matematika i Informatika, No. 62, 2019, pp. 27–33.

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Zagidullin, R.R. Solving the Transport-Coagulation Problem in a Two-Dimensional Spatial Region. Comput Math Model 31, 19–24 (2020). https://doi.org/10.1007/s10598-020-09473-z

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  • DOI: https://doi.org/10.1007/s10598-020-09473-z

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