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

  1. V. M. Goloviznin and A. A. Samarskii, “Finite Difference Approximation of Convective Transport Equation with Space Splitting Time Derivative,” Mat. Model. 10 (1), 86-100 (1998).
  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

08-05-2018

How to Cite

Соловьев А., Данилин А. A Higher-Order Difference Scheme of the Cabaret Class for Solving the Transport Equation // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2018. 19. 185-193. doi 10.26089/NumMet.v19r217

Issue

Section

Section 1. Numerical methods and applications

Most read articles by the same author(s)