高阶近似的三维网格特征格式

IF 0.5 4区 数学 Q3 MATHEMATICS
I. B. Petrov, V. I. Golubev, A. V. Shevchenko, A. Sharma
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引用次数: 0

摘要

本文研究了全三维情况下地震波的传播。在实际应用中,地震勘探过程中地质介质的应力-应变状态经常使用声学和线弹性模型来描述。两种模型的偏微分方程控制系统均为线性双曲型。应用网格特征方法可以构造出它们的计算算法。在多维问题中,维度分裂起着重要的作用。然而,即使在使用扩展空间模板来解决由此产生的一维问题的情况下,最终的三维方案也未能保持所获得的高阶。在本文中,我们提出了一种基于多阶段算子分裂格式的方法,使构造三阶三维网格特征格式成为可能。对几个测试问题进行了数值求解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Three-Dimensional Grid-Characteristic Schemes of High Order of Approximation

Three-Dimensional Grid-Characteristic Schemes of High Order of Approximation

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.

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来源期刊
Doklady Mathematics
Doklady Mathematics 数学-数学
CiteScore
1.00
自引率
16.70%
发文量
39
审稿时长
3-6 weeks
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 It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications.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.
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