TY - JOUR
T1 - Three-Layer Non-Hydrostatic Staggered Scheme for Free Surface Flow
AU - Ade C. Bayu, S. R. Pudjaprasetya & I. Magdalena
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 643
EP - 657
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.171016.300517a
UR - https://global-sci.org/intro/article_detail/eajam/10711.html
KW - The 2D Euler equations, non-hydrostatic scheme, solitary wave, undular bore.
AB - <p style="text-align: justify;">In this paper, a finite difference algorithm using a three-layer approximation
for the vertical flow region to solve the 2D Euler equations is considered. In this algorithm,
the pressure is split into hydrostatic and hydrodynamic parts, and the predictor-corrector
procedure is applied. In the predictor step, the momentum hydrostatic model
is formulated. In the corrector step, the hydrodynamic pressure is accommodated after
solving the Laplace equation using the Successive Over Relaxation (SOR) iteration
method. The resulting algorithm is first tested to simulate a standing wave over an intermediate
constant depth. Dispersion relation of the scheme is derived, and it is shown to
agree with the analytical dispersion relation for kd &lt; π with 94% accuracy. The second
test case is a solitary wave simulation. Our computed solitary wave propagates with constant
velocity, undisturbed in shape, and confirm the analytical solitary wave. Finally,
the scheme is tested to simulate the appearance of the undular bore. The result shows a
good agreement with the result from the finite volume scheme for the Boussinesq-type
model by Soares-Frazão and Guinot (2008).</p>