I. B. Petrov, V. I. Golubev, A. V. Shevchenko, A. Sharma
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引用次数: 0
Abstract
This paper examines seismic wave propagation in a full three-dimensional case. In practice, the stress-strain state of a geological medium during seismic exploration is frequently described using acoustic and linear elastic models. The governing systems of partial differential equations of both models are linear hyperbolic. A computational algorithm for them can be constructed by applying a grid-characteristic approach. In the case of multidimensional problems, an important role is played by dimensional splitting. However, the final three-dimensional scheme fails to preserve the achieved high order even in the case of extended spatial stencils used to solve the resulting one-dimensional problems. In this paper, we propose an approach based on multistage operator splitting schemes, which made it possible to construct a three-dimensional grid-characteristic scheme of the third order. Several test problems are solved numerically.
期刊介绍:
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.