Compact difference schemes for convection-diffusion equations
https://doi.org/10.29235/1561-2430-2021-57-3-311-318
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.
Supporting agencies: The author is very grateful to Professor P. P. Matus for help in this work.
About the Author
B. D. Utebaev
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Utebaev Bakhadir Dauletbay uli – Postgraduate Student
11, Surganov Str., 220072, Minsk
References
1. Samarskii A. A. Schemes of high-order accuracy for the multi-dimensional heat conduction equation. Computational Mathematics and Mathematical Physics, 1963, vol. 3, no. 5, pp. 1107–1146. https://doi.org/10.1016/0041-5553(63)90104-6
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
6. Karetkina N. V. An unconditionally stable difference scheme for parabolic equations containing first derivatives. Computational Mathematics and Mathematical Physics, 1980, vol. 20, no. 1, pp. 257–262. https://doi.org/10.1016/0041-5553(80)90078-6
7. Samarskii A. A., Vabishchevich P. N. Numerical Methods for Solving Convection-Diffusion Problems. Moscow, Editorial URSS Publ., 1999. 248 p. (in Russian).
8. Samarskii A. A. Theory of Difference Schemes. New York, Marcel Dekker Inc., 2001. https://doi.org/10.1201/9780203908518
9. Samarskii A. A., Vabishchevich P. N., Matus P. P. Difference Schemes with Operator Factors. Minsk, TsOTZh Publ., 1998, 432 p. (in Russian).
10. Samarskii A. A., Andreev V. B. Difference Methods for Elliptic Equations. Moscow, Nauka Publ., 1976, 352 p. (in Russian).
11. Matus P. P., Utebaev B. D. Compact and monotone difference schemes for parabolic equations. Matematicheskoe modelirovanie = Mathematical Models and Computer Simulations, 2021, vol. 33, no. 4, pp. 60–78 (in Russian). https://doi.org/10.20948/mm-2021-04-04
12. Tingchun Wang. Convergence of an eight-order compact difference scheme for the nonlinear Schrodinger equation. Advances in Numerical Analysis, 2012, vol. 2012, pp. 1–24. https://doi.org/10.1155/2012/913429
13. Matus P. P., Anh H. T. K. Compact difference schemes for Klein-Gordon equation. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2020, vol. 64, no. 5, pp. 526–533 (in Russian). http://doi.org/10.29235/1561-8323-2020-64-5-526-533
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