Linear Quasi-Monotone and Hybrid Grid-Characteristic Schemes for the Numerical Solution of Linear Acoustic Problems1

The system of linear acoustic equations is hyperbolic. It describes the process of acoustic wave propagation in deformable media. An important property of the schemes used for the numerical solution is their high approximation order. This property allows one to simulate the perturbation propagation...

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Bibliographic Details
Published in:Numerical analysis and applications 2023-06, Vol.16 (2), p.112-122
Main Authors: Guseva, E. K., Golubev, V. I., Petrov, I. B.
Format: Article
Language:English
Subjects:
Acoustic propagation
Acoustic properties
Acoustic waves
Acoustics
Computational grids
Formability
Longitudinal waves
Mathematics
Mathematics and Statistics
Numerical Analysis
Perturbation
Transport equations
Wave propagation
Wave reflection
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Summary:The system of linear acoustic equations is hyperbolic. It describes the process of acoustic wave propagation in deformable media. An important property of the schemes used for the numerical solution is their high approximation order. This property allows one to simulate the perturbation propagation process over sufficiently large distances. Another important property is schemes’ monotonicity, which prevents the appearance of non-physical oscillations in the solution. In this paper, we present linear quasi-monotone and hybrid grid-characteristic schemes for a linear transport equation and a system of one-dimensional linear acoustic equations. They are constructed by a method of analysis in the space of unknown coefficients proposed by A.S. Kholodov based on the grid-characteristic monotonicity criterion. Wide spatial stencils with five to seven computational grid nodes are considered. Reflection of a longitudinal wave with a sharp front from the interface between media with different parameters is used as a test to compare the obtained numerical solutions.
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423923020027