Nonhydrostatic models have proven their superiority in describing tsunami propagation over trans-oceanic distances and nearshore transformation because of their good dispersion and nonlinearity properties. The novel one-layer nonhydrostatic formulations proposed by Wang et al. [Phys. Fluids 35, 076610 (2023)] have been rederived in the spherical coordinate system incorporating Coriolis effects to enable the application of basin-wide tsunami propagation. The model was implemented using the fractional step method, where the hydrostatic step was solved by a Godunov-type finite-volume scheme, and the nonhydrostatic step was obtained with the finite-difference method. Additionally, a two-way grid-nesting scheme was employed to adapt the topographic features for efficient computation of tsunami propagation in deep ocean and coastal inundation. Furthermore, graphics processing unit (GPU)-parallelism technique was incorporated to further optimize the model performance. An idealized benchmark test as well as three experiments of regular and irregular waves, solitary, and N-waves transformations have been simulated to demonstrate the superior performance of the current GPU-accelerated grid-nesting nonhydrostatic model. Finally, the model has been applied to reproduce the 1964 Prince William Sound Tsunami, its propagation across the North Pacific and induced inundation in the Seaside.
REFERENCES
1.
H.
Wang
,
G.
Wang
,
J.
Zheng
,
Q.
Liang
, and
A.
Tao
, “
Advancements in nearshore wave modeling: A unified one-layer nonhydrostatic approach
,” Phys. Fluids
35
, 076610
(2023
).2.
V.
Titov
,
U.
Kânoğlu
, and
C.
Synolakis
, “
Development of MOST for real-time tsunami forecasting
,” J. Waterway Port Coastal Ocean Eng.
142
, 03116004
(2016
).3.
F.
Imamura
, Review of Tsunami Simulation with a Finite Difference Method
(
World Scientific
,
Singapore
, 1997
).4.
P. L. F.
Liu
,
Y. S.
Cho
,
M. J.
Briggs
,
U.
Kanoglu
, and
C. E.
Synolakis
, “
Runup of solitary waves on a circular Island
,” J. Fluid Mech.
302
, 259
(1995
).5.
J.
Horrillo
,
Z.
Kowalik
, and
Y.
Shigihara
, “
Wave dispersion study in the Indian Ocean-Tsunami of December 26, 2004
,” Mar. Geodesy
29
, 149
(2006
).6.
C.
Ai
,
Y.
Ma
,
C.
Yuan
,
Z.
Xie
, and
G.
Dong
, “
A three-dimensional non-hydrostatic model for tsunami waves generated by submarine landslides
,” Appl. Math. Model.
96
, 1
(2021
).7.
C.
Ai
,
Y.
Ma
,
W.
Ding
,
Z.
Xie
, and
G.
Dong
, “
An efficient three-dimensional non-hydrostatic model for undular bores in open channels
,” Phys. Fluids
33
, 127111
(2021
).8.
G.
Wang
,
J.
Zheng
, and
Q.
Liang
, “
Accuracy of depth-integrated nonhydrostatic wave models
,” Ocean Eng.
149
, 217
(2018
).9.
M.
Zijlema
,
G.
Stelling
, and
P.
Smit
, “
SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters
,” Coastal Eng.
58
, 992
(2011
).10.
R. A.
Walters
, “
A semi-implicit finite element model for non-hydrostatic (dispersive) surface waves
,” Int. J. Numer. Meth. Fluids
49
, 721
(2005
).11.
O. B.
Fringer
,
M.
Gerritsen
, and
R. L.
Street
, “
An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator
,” Ocean Model.
14
, 139
(2006
).12.
Y.
Yamazaki
,
Z.
Kowalik
, and
K. F.
Cheung
, “
Depth-integrated, non-hydrostatic model for wave breaking and run-up
,” Numer. Methods Fluids
61
, 473
(2009
).13.
C.
Ai
,
Y.
Ma
,
W.
Ding
,
Z.
Xie
, and
G.
Dong
, “
Three-dimensional non-hydrostatic model for dam-break flows
,” Phys. Fluids
34
, 022105
(2022
).14.
C.-C.
Young
,
C. H.
Wu
,
J.-T.
Kuo
, and
W.-C.
Liu
, “
A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves
,” Ocean Eng.
34
, 1357
(2007
).15.
G.
Ma
,
F.
Shi
, and
J. T.
Kirby
, “
Shock-capturing non-hydrostatic model for fully dispersive surface wave processes
,” Ocean Model.
43–44
, 22
(2012
).16.
G.
Ran
,
Q.
Zhang
,
G.
Shi
, and
X.
Li
, “
A new Poisson-type equation applicable to the three-dimensional non-hydrostatic model in the framework of the discontinuous Galerkin method
,” Comput. Math. Appl.
145
, 13
(2023
).17.
Y.
Yamazaki
,
K. F.
Cheung
, and
Z.
Kowalik
, “
Depth-integrated, non-hydrostatic model with grid nesting for tsunami generation, propagation, and run-up
,” Numer. Methods Fluids
67
, 2081
(2011
).18.
Y.
Bai
and
K. F.
Cheung
, “
Hydrostatic versus non-hydrostatic modeling of tsunamis with implications for insular shelf and reef environments
,” Coastal Eng.
117
, 32
(2016
).19.
T. Q.
Chen
and
Q. H.
Zhang
, “
GPU acceleration of a nonhydrostatic model for the internal solitary waves simulation
,” J. Hydrodyn.
25
, 362
(2013
).20.
F.
Shi
,
J. T.
Kirby
,
G.
Ma
, and
B.
Tehranirad
, “
Non-hydrostatic wave model NHWAVE: User's guide for modeling submarine landslide tsunami (version 1.1)
,” Research Report NO. CACR-12-04
, 2012
.21.
Q.
Liang
and
L. S.
Smith
, “
A high-performance integrated hydrodynamic modelling system for urban flood simulations
,” J. Hydroinformatics
17
, 518
(2015
).22.
C.
Escalante
,
T. M. d
Luna
, and
M. J.
Castro
, “
Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme
,” Appl. Math. Comput.
338
, 631
(2018
).23.
C.
Ai
,
Y.
Ma
,
C.
Yuan
, and
G.
Dong
, “
Development and assessment of semi-implicit nonhydrostatic models for surface water waves
,” Ocean Model.
144
, 101489
(2019
).24.
Z.
Kowalik
,
W.
Knight
, and
T.
Logan
, Numerical Modeling of Ocean Dynamics
(
World Scientific
, 1993
).25.
Q.
Liang
and
F.
Marche
, “
Numerical resolution of well-balanced shallow water equations with complex source terms
,” Adv. Water Resources
32
, 873
(2009
).26.
Q.
Liang
and
A. G. L.
Borthwick
, “
Adaptive quadtree simulation of shallow flows with wet–dry fronts over complex topography
,” Comput. Fluids
38
, 221
(2009
).27.
Y. K.
Choi
,
F.
Shi
,
M.
Malej
,
J. M.
Smith
,
J. T.
Kirby
, and
S. T.
Grilli
, “
Block-structured, equal-workload, multi-grid-nesting interface for the Boussinesq wave model FUNWAVE-TVD (Total Variation Diminishing)
,” Geosci. Model Dev.
15
, 5441
(2022
).28.
M.
Herzfeld
and
F.
Rizwi
, “
A two-way nesting framework for ocean models
,” Environ. Model. Software
117
, 200
(2019
).29.
K.
Fang
,
J.
Sun
,
G.
Song
,
G.
Wang
,
H.
Wu
, and
Z.
Liu
, “
A GPU accelerated Boussinesq-type model for coastal waves
,” Acta Oceanol. Sin.
41
, 158
(2022
).30.
C.
Escalante
,
M.
Dumbser
, and
M. J.
Castro
, “
An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes
,” J. Comput. Phys.
394
, 385
(2019
).31.
E. F.
Toro
,
M.
Spruce
, and
W.
Speares
, “
Restoration of the contact surface in the HLL-Riemann solver
,” Shock Waves
4
, 25
(1994
).32.
J.-I.
Lee
,
Y.-T.
Kim
, and
Y.-S.
Cho
, “
Hydraulic experiments for wave transformation over a submerged elliptic shoal
,” J. Coastal Res.
291
, 196
(2013
).33.
P.
Lynett
,
D.
Swigler
,
S.
Son
,
D.
Bryant
, and
S.
Socolofsky
, Experimental Study of Solitary Wave Evolution over a 3D Shallow Shelf
(
American Society of Civil Engineers (ASCE)
,
Shanghai, China
, 2010
).34.
M.
Matsuyama
and
H.
Tanaka
, “
An experimental study of the highest run-up height in the 1993 Hokkaido Nansei-Oki earthquake tsunami
,” in International Tsunami Symposium
, Seattle, USA, 2001
.35.
Y.
Okada
, “
Surface deformation due to shear and tensile faults in a half-space
,” Bull. Seismol. Soc. Am.
75
, 1135
(1985
).36.
J. M.
Johnson
,
K.
Satake
,
S. R.
Holdahl
, and
J.
Sauber
, “
The 1964 Prince William Sound earthquake: Joint inversion of tsunami and geodetic data
,” J. Geophys. Res.
101
, 523
, https://doi.org/10.1029/95JB02806 (1996
).37.
G.
Wang
,
Q.
Liang
,
F.
Shi
, and
J.
Zheng
, “
Analytical and numerical investigation of trapped ocean waves along a submerged ridge
,” J. Fluid Mech.
915
, A54
(2021
).38.
F. I.
González
,
E. L.
Geist
,
B.
Jaffe
,
U.
Kânoğlu
,
H.
Mofjeld
,
C. E.
Synolakis
,
V. V.
Titov
,
D.
Arcas
,
D.
Bellomo
,
D.
Carlton
,
T.
Horning
,
J.
Johnson
,
J.
Newman
,
T.
Parsons
,
R.
Peters
,
C.
Peterson
,
G.
Priest
,
A.
Venturato
,
J.
Weber
,
F.
Wong
, and
A.
Yalciner
, “
Probabilistic tsunami hazard assessment at Seaside, Oregon, for near- and far-field seismic sources
,” J. Geophys. Res.
114
, C11023
, https://doi.org/10.1029/2008jc005132 (2009
).39.
Y.
Bai
and
K. F.
Cheung
, “
Dispersion and nonlinearity of multi-layer non-hydrostatic free-surface flow
,” J. Fluid Mech.
726
, 226
(2013
).40.
Z. B.
Liu
,
K. Z.
Fang
, and
Y. Z.
Cheng
, “
A new multi-layer irrotational Boussinesq-type model for highly nonlinear and dispersive surface waves over a mildly sloping seabed
,” J. Fluid Mech.
842
, 323
(2018
).41.
P.
Lynett
and
P. L. F.
Liu
, “
A two-layer approach to wave modelling
,” Proc. R Soc. Lond. A
460
, 2637
(2004
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
