Implicit and time reversible CABARET schemes for quasilinear shallow water equations

Authors

  • V.M. Goloviznin Nuclear Safety Institute (IBRAE) of RAS
  • D.Yu. Gorbachev Lomonosov Moscow State University
  • A.M. Kolokolnikov Lomonosov Moscow State University
  • P.A. Maiorov Lomonosov Moscow State University
  • B.A. Tlepsuk Lomonosov Moscow State University

DOI:

https://doi.org/10.26089/NumMet.v17r437

Keywords:

CABARET scheme, shallow water equations, conservative schemes, time reversible schemes, numerical simulation

Abstract

A new implicit unconditionally stable scheme for the one-dimensional shallow water equations is proposed. This implicit scheme retains all the features of the explicit CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) difference scheme. Dissipative and dispersion properties of this new scheme are analyzed; an algorithm of its numerical solution is discussed. Some examples of solving the Riemann problem are considered.

Author Biographies

V.M. Goloviznin

Nuclear Safety Institute (IBRAE) of RAS
• Head of Department

D.Yu. Gorbachev

Lomonosov Moscow State University
• Student

A.M. Kolokolnikov

Lomonosov Moscow State University
• Student

P.A. Maiorov

Lomonosov Moscow State University
• Student

B.A. Tlepsuk

Lomonosov Moscow State University
• Student

References

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Published

27-09-2016

How to Cite

Головизнин В., Горбачев Д., Колокольников А., Майоров П., Тлепсук Б. Implicit and Time Reversible CABARET Schemes for Quasilinear Shallow Water Equations // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2016. 17. 402-414. doi 10.26089/NumMet.v17r437

Issue

Vol. 17 (2016): Issue 4.

Section

Section 1. Numerical methods and applications