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Application of the CABARE scheme for numerical simulation of two-dimensional thermal convection
| Title | Application of the CABARE scheme for numerical simulation of two-dimensional thermal convection |
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| Authors | M. S. Eroshkina1, V. M. Goloviznin1, Y. N. Deryugin1 1Branch of Lomonosov Moscow State University in Sarov |
| Annotation | Thermal convection plays an important role in many fields, from construction and electronics to nuclear power and space technology. In this regard, an urgent task of computational fluid dynamics is the development of methods that improve the accuracy of modeling thermal convection while maintaining stability and moderate computational costs. Despite the variety of existing numerical methods, including high-order schemes, the methods of the second order of accuracy remain the most in demand: they provide a balance of accuracy, stability and ease of implementation. In this regard, the CABARE scheme is of particular interest due to its simple implementation, second–order approximation on a compact computational template, and good dissipative-dispersion characteristics. In this paper, a new explicit-implicit technique based on the "CABARE" scheme is proposed for numerical modeling of convective heat transfer in two-dimensional regions, using the weak compressibility approximation and applied to both planar and axisymmetric problem statements. |
| Keywords | mathematical modeling, numerical methods, CABARET scheme. |
| Citation | Eroshkina M. S., Goloviznin V. M., Deryugin Y. N. ''Application of the CABARE scheme for numerical simulation of two-dimensional thermal convection'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 74-76. Available at: https://conf.svmo.ru/files/2026/papers/paper77.pdf. - Date of access: 25.09.2026. |
© SVMO, National Research Mordovia State University, 2026
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