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)


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.


Two-phase filtering problem Finite difference schemes Computer simulations 



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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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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