DOI: https://doi.org/10.26089/NumMet.v20r105

Using the Sharp scheme of higher-order accuracy for solving some nonlinear hyperbolic systems of equations

Authors

  • A.V. Solovjev
  • A.V. Danilin

Keywords:

Cabaret method
Sharp scheme
hyperbolic equations
high-accuracy schemes

Abstract

The Sharp difference scheme of higher-order accuracy developed previously for solving the scalar one-dimensional transport equation is extended to the shallow water nonlinear systems and to the systems of Euler equations using the balance-characteristic approach. For these systems, a number of test problems are solved to illustrate the features of the solutions obtained by the described difference scheme.

New computational technologies

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Published

2019-02-13

Issue

Vol. 20 (2019): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

A.V. Solovjev

Nuclear Safety Institute (IBRAE) of RAS
• Leading Researcher

A.V. Danilin

Nuclear Safety Institute (IBRAE) of RAS
• Junior Researcher

References

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  3. V. M. Goloviznin and B. N. Chetverushkin, “New Generation Algorithms for Computational Fluid Dynamics,” Zh. Vychisl. Mat. Mat. Fiz. 58 (8), 20-29 (2018) [Comput. Math. Math. Phys. 58 (8), 1217-1225 (2018)].
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    doi 10.2514/6.2011-3840
  6. A. V. Solovjev A.V. and A. V. Danilin, “A Higher-Order Difference Scheme of the Cabaret Class for Solving the Transport Equation,” Vychisl. Metody Programm. 19, 185-193 (2018).