TY - JOUR
T1 - Dispersive Shallow Water Wave Modelling. Part IV: Numerical Simulation on a Globally Spherical Geometry
AU - Gayaz Khakimzyanov, Denys Dutykh & Oleg Gusev
JO - Communications in Computational Physics
VL - 2
SP - 361
EP - 407
PY - 2018
DA - 2018/02
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2016-0179d
UR - https://global-sci.org/intro/article_detail/cicp/10530.html
KW - Finite volumes, splitting method, nonlinear dispersive waves, spherical geometry, rotating sphere, Coriolis force.
AB - <p style="text-align: justify;">In the present manuscript we consider the problem of dispersive wave simulation
on a rotating globally spherical geometry. In this Part IV we focus on numerical
aspects while the model derivation was described in Part III. The algorithm we
propose is based on the splitting approach. Namely, equations are decomposed on a
uniform elliptic equation for the dispersive pressure component and a hyperbolic part
of shallow water equations (on a sphere) with source terms. This algorithm is implemented
as a two-step predictor-corrector scheme. On every step we solve separately
elliptic and hyperbolic problems. Then, the performance of this algorithm is illustrated
on model idealized situations with even bottom, where we estimate the influence of
sphericity and rotation effects on dispersive wave propagation. The dispersive effects
are quantified depending on the propagation distance over the sphere and on the linear
extent of generation region. Finally, the numerical method is applied to a couple
of real-world events. Namely, we undertake simulations of the BULGARIAN 2007 and
CHILEAN 2010 tsunamis. Whenever the data is available, our computational results
are confronted with real measurements.</p>