A higher-order difference scheme of the Cabaret class for solving the transport equation

Authors

DOI:

https://doi.org/10.26089/NumMet.v19r217

Keywords:

Cabaret scheme, transport equation, higher order approximation, accuracy

Abstract

A new difference scheme of the Cabaret class with a higher order of accuracy for solving the scalar transport equation is proposed. The order of approximation of this difference scheme is equal to four. The balance-characteristic representation of the scheme is constructed and the dispersion properties are given. For the proposed difference scheme, a number of examples to solve the transport equation for smooth and discontinuous profiles are considered in comparison with the classical Cabaret scheme.

Author Biographies

A.V. Solovjev

A.V. Danilin

References

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  2. V. M. Goloviznin and A. A. Samarskii, “Some Characteristics of Finite Difference Scheme ’Cabaret’,” Mat. Model. 10 (1), 101-116 (1998).
  3. A. Iserles, “Generalized Leapfrog Methods,” IMA J. Numer. Anal. 6 (4), 381-392 (1986).
  4. V. M. Goloviznin, S. A. Karabasov, and I. M. Kobrinskii, “Balance-Characteristic Schemes with Separated Conservative and Flux Variables,” Mat. Model. 15 (9), 29-48 (2003).
  5. 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].
  6. O. A. Kovyrkina and V. V. Ostapenko, “On Monotonicity of Two-Layer in Time Cabaret Scheme,” Mat. Model. 24 (9), 97-112 (2012) [Math. Models Comput. Simul. 5 (2), 180-189 (2013)].

Published

2018-05-08

How to Cite

Соловьев А.В., Данилин А.В. A Higher-Order Difference Scheme of the Cabaret Class for Solving the Transport Equation // Numerical methods and programming. 2018. 19. 185-193. doi 10.26089/NumMet.v19r217

Issue

Section

Section 1. Numerical methods and applications