Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System

Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System

Year:    2020

Author:    Alina Chertock, Yongle Liu

Communications in Computational Physics, Vol. 27 (2020), Iss. 2 : pp. 480–502

Abstract

We study the two-component Camassa-Holm (2CH) equations as a model for the long time water wave propagation. Compared with the classical Saint-Venant system, it has the advantage of preserving the waves amplitude and shape for a long time. We present two different numerical methods—finite volume (FV) and hybrid finite-volume-particle (FVP) ones. In the FV setup, we rewrite the 2CH equations in a conservative form and numerically solve it by the central-upwind scheme, while in the FVP method, we apply the central-upwind scheme to the density equation only while solving the momentum and velocity equations by a deterministic particle method. Numerical examples are shown to verify the accuracy of both FV and FVP methods. The obtained results demonstrate that the FVP method outperforms the FV method and achieves a superior resolution thanks to a low-diffusive nature of a particle approximation.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0325

Communications in Computational Physics, Vol. 27 (2020), Iss. 2 : pp. 480–502

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Two-component Camassa-Holm system finite-volume method deterministic particle method finite-volume-particle method central-upwind scheme.

Author Details

Alina Chertock

Yongle Liu