TY - JOUR
T1 - A Dispersive Numerical Model for the Formation of Undular Bores Generated by Tsunami Wave Fission 
AU - I. Magdalena
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 767
EP - 784
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.161016.300517b
UR - https://global-sci.org/intro/article_detail/eajam/10719.html
KW - Undular bores, depth integrated Euler equations, finite volume method, predictor corrector, tsunami fission.
AB - <p style="text-align: justify;">A two-layer non-hydrostatic numerical model is proposed to simulate the
formation of undular bores by tsunami wave fission. These phenomena could not be
produced by a hydrostatic model. Here, we derived a modified Shallow Water Equations
with involving hydrodynamic pressure using two layer approach. Staggered finite
volume method with predictor corrector step is applied to solve the equation numerically.
Numerical dispersion relation is derived from our model to confirm the exact
linear dispersion relation for dispersive waves. To illustrate the performance of our non-hydrostatic
scheme in case of linear wave dispersion and non-linearity, four test cases
of free surface flows are provided. The first test case is standing wave in a closed basin,
which test the ability of the numerical scheme in simulating dispersive wave motion
with the correct frequency. The second test case is the solitary wave propagation as the
examination of owing balance between dispersion and nonlinearity. Regular wave propagation
over a submerged bar test by Beji is simulated to show that our non-hydrostatic
scheme described well the shoaling process as well as the linear dispersion compared
with the experimental data. The last test case is the undular bore propagation.</p>