Abstract
The aim of the study is the development of the implicit grid-characteristic method on structured grids in problems related to linearly elastic medium. We consider how grid-characteristic method builds and adapts boundary conditions to implicit method. Obtained method is tested in one- and two-dimensional model problems. We investigate the grid convergence and stability of the derived algorithm for Courant numbers greater than 1 under the conditions of a one-dimensional problem. As a result of numerical simulation in two dimensions, patterns of the distribution of the vertical component velocity are obtained for different types of calculation methods: implicit and explicit–implicit. The obtained patterns are compared with the explicit grid-characteristic calculation method from the RECT package. According to the obtained results, implicit grid-characteristic method is applicable to the long-term dynamic and static problem, but first-order implicit methods have a solution blur.
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Acknowledgements
This work has been performed with the financial support of the Russian Science Foundation (project No. 20-71-10028).
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Pesnya, E., Kozhemyachenko, A.A., Favorskaya, A.V. (2021). Application of Implicit Grid-Characteristic Methods for Modeling Wave Processes in Linear Elastic Media. In: Czarnowski, I., Howlett, R.J., Jain, L.C. (eds) Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 238. Springer, Singapore. https://doi.org/10.1007/978-981-16-2765-1_12
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DOI: https://doi.org/10.1007/978-981-16-2765-1_12
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