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Construction of Higher-Order Approximation Difference Scheme for Nonlinear Convection-Diffusion Equation Using Adaptive Artificial Viscosity in Case of Two-Phase Filtering Problems

  • I. V. PopovEmail author
  • Yu. A. Poveshchenko
  • S. V. Polyakov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

The method of adaptive artificial viscosity is used to model the process of one-dimensional nonlinear convection-diffusion equation. For this purpose, a finite difference scheme (FDS) of the second order of time and space approximation has been developed. The scheme was tested using a numerical solution of the problem on formation of a gradient catastrophe. The process of two-phase filtration was analyzed with the help of constructed FDS. Numerical calculations showed that the proposed method, and in this case reliably tracks the discontinuities of the solution.

Keywords

Two-phase filtering problem Finite difference schemes Computer simulations 

Notes

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (projects Nos. 16-07-00519-a, 18-07-00841-a, 16-29-15095-ofi-m).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Keldysh Institute of Applied Mathematics of RAS, 4 Miusskaya squareMoscowRussia
  2. 2.National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

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