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Actual Accuracy of Linear Schemes of High-Order Approximation in Gasdynamic Simulations

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Abstract

A new test problem for one-dimensional gas dynamics equations is considered. Initial data in the problem is a periodic smooth wave. Shock waves are formed in the gas flow over a finite time. The convergence under mesh refinement is analyzed for two third-order accurate linear schemes, namely, a bicompact scheme and Rusanov’s scheme. It is demonstrated that both schemes have only the first order of integral convergence in the shock influence area. However, when applied to equations of isentropic gas dynamics, the schemes converge with at least the second order.

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Funding

This work was supported by the Moscow Center of Fundamental and Applied Mathematics, agreement no. 075-15-2022-283 with the Ministry of Science and Higher Education of the Russian Federation (Section 4) and by the Russian Science Foundation, project no. 22-11-00060 (Section 5).

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Authors and Affiliations

  1. Federal research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    M. D. Bragin

  2. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    M. D. Bragin

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Translated by I. Ruzanova

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Bragin, M.D. Actual Accuracy of Linear Schemes of High-Order Approximation in Gasdynamic Simulations. Comput. Math. and Math. Phys. 64, 138–150 (2024). https://doi.org/10.1134/S0965542524010044

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