TY - JOUR
T1 - Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System
AU - Chertock , Alina
AU -  , 
AU - Liu , Yongle
JO - Communications in Computational Physics
VL - 2
SP - 480
EP - 502
PY - 2019
DA - 2019/12
SN - 27
DO - http://doi.org/10.4208/cicp.OA-2018-0325
UR - https://global-sci.org/intro/article_detail/cicp/13455.html
KW - Two-component Camassa-Holm system, finite-volume method, deterministic particle method, finite-volume-particle method, central-upwind scheme.
AB - <p style="text-align: justify;">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.</p>