1. Ingram D. M., Causon D. M., Mingham C. G. Developments in cartesian cut cell methods. Mathematics and Computers in Simulation, 2003, vol. 61, no. 3-6, pp. 561-572. https://doi.org/10.1016/s0378-4754(02)00107-6
2. Kirkpatrick M. P., Armfield S. W., Kent J. H. A representation of curved boundaries for the solution of the Navier- Stokes equations on a staggered three-dimensional Cartesian grid. Journal of Computational Physics, 2003, vol. 184, no. 1, pp. 1-36. https://doi.org/10.1016/s0021-9991(02)00013-x
3. Ye T., Mittal R., Udaykumar H. S., Shyy W. An accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries. Journal of Computational Physics, 1999, vol. 156, no. 2, pp. 209-240. https://doi.org/10.1006/jcph.1999.6356
4. Mittal R., Iaccarino G. Immersed boundary methods. Annual Review of Fluid Mechanics, 2005, vol. 37, pp. 239-261. https://doi.org/10.1146/annurev.fluid.37.061903.175743
5. LeVeque R. J., Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM Journal on Numerical Analysis, 1994, vol. 31, no. 4, pp. 1019-1044. https://doi.org/10.1137/0731054
6. Li Z. An overview of the immersed interface method and its applications. Taiwanese Journal of Mathematics, 2003, vol. 7, no. 1, pp. 1-49. https://doi.org/10.11650/twjm/1500407515
7. Vabishchevich P. N. Method of Fictitious Domains in the Problems of Mathematical Physics. Moscow, Moscow University Publishing House, 1991. 156 p. (in Russian).
8. Vinnikov V. V., Reviznikov D. L. Cartesian grids methods for numerical solution of Navier-Stokes equations in domains with curvilinear boundaries. Matematicheskoe modelirovanie = Mathematical Models and Computer Simulation, 2005, vol. 17, no. 8, pp. 15-30 (in Russian).
9. Fletcher C. A. J. Computational Techniques for Fluid Dynamics. Vol. 2. Berlin, Heidelberg, Springer, 1988. 494 p. https://doi.org/10.1007/978-3-642-97071-9
10. Thompson J. F., Warsi Z. U. A., Mastin C. W. Numerical Grid Generation: Foundations and Applications. New York, Elsevier North-Holland, 1985. 483 p.
11. Mastin C. W. Error induced by coordinate systems. Applied Mathematics and Computation, 1982, vol. 10-11, pp. 31- 40. https://doi.org/10.1016/0096-3003(82)90186-2
12. Samarskii A. A. The Theory of Difference Schemes. New York, 2001. 786 p. https://doi.org/10.1201/9780203908518
13. Samarskii A. A., Andreev V. B. Difference Methods for Elliptic Equations. Moscow, Nauka Publ., 1976. 352 p. (in Russian).
14. Samarskii A., Matus P., Mazhukin V., Mozolevski I. Monotone difference schemes for equations with mixed derivatives. Computers & Mathematics with Applications, 2002, vol. 44, no. 3-4, pp. 501-510. https://doi.org/10.1016/S0898-1221(02)00164-5
15. Rybak I. Monotone and conservative difference schemes for elliptic equations with mixed derivatives. Mathematical Modelling and Analysis, 2004, vol. 9, pp. 169-178. https://doi.org/10.3846/13926292.2004.9637250
16. Matus P. P., Le Minh Hieu, Pylak D. Difference schemes for quasilinear parabolic equations with mixed derivatives. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2019, vol. 63, no. 3, pp. 263-269 (in Russian). https://doi.org/10.29235/1561-8323-2019-63-3-263-269
17. Gaspar F. J., Lisbona F. J., Matus P., Tuyen V. T. K. Monotone finite difference schemes for quasilinear parabolic problems with mixed boundary conditions. Computational Methods in Applied Mathematics, 2016, vol. 16, no. 2, pp. 231-244. https://doi.org/10.1515/cmam-2016-0002
18. Chuiko M. M., Korolyova O. M. Solution of the mixed boundary problem for the Poisson equation on two-dimensional irregular domains. Informatika = Informatics, 2023, vol. 20, no. 2, pp. 111−120 (in Russian). https://doi.org/10.37661/1816-0301-2023-20-2-111-120
19. Schneider G. E., Zedan M. A modified strongly implicit procedure for the numerical solution of field problem. Numerical Heat Transfer, 1981, vol. 4, no. 1, pp. 1-19. https://doi.org/10.1080/01495728108961775
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