THREE-DIMENSIONAL GRID CHARACTERISTIC SCHEMES OF HIGH ORDER OF APPROXIMATION

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详细

This paper examines the process of the seismic wave propagation in a full three-dimensional case. To describe the stress-strain state of a geological medium during seismic exploration, acoustic and linear elastic models are widely used in practice. The governing systems of partial differential equations of both models are linear hyperbolic. To construct a computational algorithm for solving them, a grid-characteristic approach can be used. In this case, an important question in multidimensional problems relates to the use of the splitting method. However, despite the use of extended spatial stencils to solve the resulting onedimensional problems, it is not possible to preserve the achieved approximation order when constructing the final three-dimensional scheme. In this paper, we propose an approach based on the multi-stage operator splitting schemes, which made it possible to construct a three-dimensional grid-characteristic scheme of the third approximation order. Given verification problems were solved numerically.

作者简介

I. Petrov

Moscow Institute of Physics and Technology (National Research University)

Email: petrov@mipt.ru
Corresponding Member of the RAS Dolgoprudny, Moscow Region, Russia

V. Golubev

Moscow Institute of Physics and Technology (National Research University)

Email: w.golubev@mail.ru
Dolgoprudny, Moscow Region, Russia

A. Shevchenko

Moscow Institute of Physics and Technology (National Research University); Ishlinsky Institute for Problems in Mechanics RAS

Email: alexshevchenko@phystech.edu
Dolgoprudny, Moscow Region, Russia; Moscow, Russia

A. Sharma

IPS Academy, Institute of Engineering and Science

Email: amitsharma@ipsacademy.org
Indore, India

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