Implicit and time reversible CABARET schemes for quasilinear shallow water equations


  • 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



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


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

D.Yu. Gorbachev

A.M. Kolokolnikov

P.A. Maiorov

B.A. Tlepsuk


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How to Cite

Головизнин В.М., Горбачев Д.Ю., Колокольников А.М., Майоров П.А., Тлепсук Б.А. Implicit and Time Reversible CABARET Schemes for Quasilinear Shallow Water Equations // Numerical methods and programming. 2016. 17. 402-414. doi 10.26089/NumMet.v17r437



Section 1. Numerical methods and applications