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High-Order Grid-Characteristic Method for Systems of Hyperbolic Equations with Piecewise Constant Coefficients

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Abstract

A new approach is considered for increasing the order of accuracy of the grid-characteristic method in the region of coefficient jumps. The approach is based on piecewise polynomial interpolation for schemes of the second and third orders of accuracy for the case where the interface between the media is consistent with a finite-difference grid. The method is intended for numerical simulation of the propagation of dynamic wave disturbances in heterogeneous media. Systems of hyperbolic equations with variable coefficients are used to describe the considered physical processes. The description of the numerical method and the results of its testing are given.

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ACKNOWLEDGMENTS

The authors are grateful to Yu.I. Skal’ko for useful consultations on the work.

Funding

This work was financially supported by the Russian Science Foundation, project 21-11-00139, https://rscf.ru/en/project/21-11-00139/.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700, Russia

    N. I. Khokhlov & I. B. Petrov

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  1. N. I. Khokhlov
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  2. I. B. Petrov
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Correspondence to N. I. Khokhlov or I. B. Petrov.

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Translated by V. Potapchouck

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Khokhlov, N.I., Petrov, I.B. High-Order Grid-Characteristic Method for Systems of Hyperbolic Equations with Piecewise Constant Coefficients. Diff Equat 59, 985–997 (2023). https://doi.org/10.1134/S001226612307011X

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  • DOI: https://doi.org/10.1134/S001226612307011X

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