DOI: https://doi.org/10.26089/NumMet.v18r431

Solution of the matter transport problem at high Peclet numbers

Authors

  • A.I. Sukhinov
  • Yu.V. Belova
  • A.E. Chistyakov

Keywords:

transport problem
Peclet number
CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) scheme
stability

Abstract

The aim of this work is the development of a difference scheme for solving the convection-diffusion problem at high Peclet numbers (Pe > 2). In accordance with this aim, a new difference scheme for convection is proposed and compared with several existing schemes and some stability conditions are formulated for the proposed scheme. The convection-diffusion equations are solved on the basis of this new difference scheme at various Peclet numbers.

New computational technologies

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Published

2017-09-12

Issue

Vol. 18 (2017): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biographies

A.I. Sukhinov

Don State Technical University
• Professor

Yu.V. Belova

Don State Technical University,
Faculty IT Systems and Technologites
• Junior Researcher

A.E. Chistyakov

Don State Technical University,
Faculty IT Systems and Technologites
• Professor

References

  1. A. A. Samarskii and P. N. Vabishchevich, Numerical Methods for Solving Convection-Diffusion Problems (Editorial, Moscow, 1999) [in Russian].
  2. V. M. Goloviznin and A. A. Samarskii, “Finite Difference Approximation of Convective Transport Equation with Space Splitting Time Derivative,” Mat. Model. 10 (1), 86-100 (1998).
  3. M. E. Ladonkina, O. A. Neklyudova, and V. F. Tishkin, “Application of the RKDG Method for Gas Dynamics Problems,” Mat. Model. 26 (1), 17-32 (2014) [Math. Models Comput. Simul. 6 (4), 397-407 (2014)].
  4. A. I. Sukhinov, A. E. Chistakov, and M. V. Iakobovskii, “Accuracy of the Numerical Solution of the Equations of Diffusion-Convection Using the Difference schemes of Second and Fourth Order Approximation Error,” Vestn. South Ural State Univ. Ser. Vychisl. Mat. Inf. 5 (1), 47-62 (2016).
  5. A. I. Sukhinov and Yu. V. Belova, “The Mathematical Model of Transformation of Phosphorus, Nitrogen and Silicon Forms in the Moving Turbulent Water Environment in Problems of Dynamics of Planktonic Populations,” Inzhener. Vestn. Dona 37 (3), 50 (2015).
  6. A. I. Sukhinov, D. S. Khachunts, and A. E. Chistyakov, “A Mathematical Model of Pollutant Propagation in Near-Ground Atmospheric Layer of a Coastal Region and Its Software Implementation,” Zh. Vychisl. Mat. Mat. Fiz. 55 (7), 1238-1254 (2015) [Comput. Math. Math. Phys. 55 (7), 1216-1231 (2015)].
  7. A. I. Sukhinov, A. V. Nikitina, and A. E. Chistyakov, “Numerical Simulation of Biological Remediation of Azov Sea,” Mat. Model. 24 (9), 3-21 (2012).

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