Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System (Communications in Computational Physics, 2019)
We study the two-component Camassa-Holm (2CH) equations as a modelfor the long time water wave propagation. Compared with the classical Saint-Venantsystem, it has the advantage of preserving the waves amplitude and shape for a longtime. We present two different numerical methods—finite volume (FV) and hybridfinite-volume-particle (FVP) ones. In the FV setup, we rewrite the 2CH equations in aconservative form and numerically solve it by the central-upwind scheme, while in theFVP method, we apply the central-upwind scheme to the density equation only whilesolving the momentum and velocity equations by a deterministic particle method. Numerical examples are shown to verify the accuracy of both FV and FVP methods. Theobtained results demonstrate that the FVP method outperforms the FV method andachieves a superior resolution thanks to a low-diffusive nature of a particle approximation.