Compact difference schemes for convection-diffusion equations

Author:

Utebaev B. D.1

Affiliation:

1. Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract

This work is devoted to the construction of compact difference schemes for convection-diffusion equations with divergent and nondivergent convective terms. Stability and convergence in the discrete norms are proved. The obtained results are generalized to multidimensional convection-diffusion equations. The test numerical calculations presented in the work are consistent with the theoretical conclusions.

Publisher

Publishing House Belorusskaya Nauka

Subject

General Medicine

Reference13 articles.

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2. Tolstykh A. I. Compact Difference Schemes and Their Use in Problems of Aerohydrodynamics. Moscow, Nauka Publ., 1990. 230 p. (in Russian).

3. Paasonen V. I. Generalization of high-precision methods for second-order nonlinear equations in orthogonal coordinate systems. Chislennye metody mekhaniki sploshnoi sredy [Numerical Methods of Continuum Mechanics], 1977, vol. 8, no. 2, pp. 94–99 (in Russian).

4. Paasonen V. I. Compact schemes for systems of second-order equations with convective terms. Vychislitelnye tekhnologii = Computational Technologies, 1998, vol. 3, no. 1, pp. 55–66 (in Russian).

5. Liao W., Zhu Jianping. A fourth-order compact finite difference scheme for solving unsteady convection-diffusion equations. Computational Simulations and Applications, 2011, pp. 81–96. https://doi.org/10.5772/25149

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