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

Authors

DOI:

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

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.

Author Biographies

A.V. Solovjev

A.V. Danilin

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)].
  4. V. M. Goloviznin, M. A. Zaitsev, S. A. Karabasov, and I. A. Korotkin, New CFD Algorithms for Multiprocessor Computer Systems (Mosk. Gos. Univ., Moscow, 2013) [in Russian].
  5. T. A. Eymann and P. L. Roe, “Active Flux Schemes for Systems,” in Proc. 20th AIAA Computational Fluid Dynamics Conference, Honolulu, Hawaii, USA, June 27-30, 2011. 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).

Published

2019-02-13

How to Cite

Соловьев А.В., Данилин А.В. Using the Sharp Scheme of Higher-Order Accuracy for Solving Some Nonlinear Hyperbolic Systems of Equations // Numerical methods and programming. 2019. 20. 45-53. doi 10.26089/NumMet.v20r105

Issue

Section

Section 1. Numerical methods and applications