Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

A. V. Shevchenko; Шевченко А. В.; V. I. Golubev; Голубев В. И.

doi:10.31857/S0044466923100137

Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

Authors: Shevchenko A.V.¹^,2, Golubev V.I.¹^,2
Affiliations:
1. Moscow Institute of Physics and Technology (National Research University)
2. Institute of Computer Aided Design, Russian Academy of Sciences
Issue: Vol 63, No 10 (2023)
Pages: 1600-1613
Section: ОБЩИЕ ЧИСЛЕННЫЕ МЕТОДЫ
URL: https://journals.rcsi.science/0044-4669/article/view/140284
DOI: https://doi.org/10.31857/S0044466923100137
EDN: https://elibrary.ru/MRAVKW
ID: 140284

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Abstract
About the authors
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Abstract

Seismic wave propagation through geological media is described by linear hyperbolic systems of equations. They correspond to acoustic, isotropic, and anisotropic linear elastic porous fluid-saturated models. They can be solved numerically by applying grid-characteristic schemes, which take into account propagation of solution discontinuities along characteristics. An important property of schemes used in practice is their high order of accuracy, due to which signal wavefronts can be clearly resolved. Previously, much attention was given to this property at interior points of the computational domain. In this paper, we study the order of a scheme up to the boundary of the domain inclusive. An approach is proposed whereby arbitrary linear boundary and contact conditions can be set up to high accuracy. The presentation is given for the system of one-dimensional acoustic equations with constant coefficients.

Keywords

grid-characteristic method, boundary conditions, contact conditions, acoustic equations

About the authors

A. V. Shevchenko

Moscow Institute of Physics and Technology (National Research University); Institute of Computer Aided Design, Russian Academy of Sciences

Email: w.golubev@mail.ru
141701, Dolgoprudnyi, Moscow oblast, Russia; 123056, Moscow, Russia

V. I. Golubev

Moscow Institute of Physics and Technology (National Research University); Institute of Computer Aided Design, Russian Academy of Sciences

Author for correspondence.
Email: w.golubev@mail.ru
Russian Federation, Moscow Region, Dolgoprudny; Russian Federation, Moscow

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