pith. sign in

arxiv: 2606.27562 · v1 · pith:UYXDIYXXnew · submitted 2026-06-25 · ⚛️ physics.flu-dyn · cs.NA· math.NA

Two-Dimensional Locally Adaptive Non-Hydrostatic Extension of Shallow Water Equations

Kemal Firdaus , J\"orn Behrens This is my paper

Pith reviewed 2026-06-29 00:38 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn cs.NAmath.NA
keywords non-hydrostatic correctionshallow water equationslocal adaptationtsunami simulationwave dispersioncomputational efficiencypredictor-corrector scheme
0
0 comments X

The pith

Locally applying non-hydrostatic corrections to shallow water equations reduces computational cost by about 40% in tsunami-like scenarios without loss of accuracy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors introduce a two-dimensional non-hydrostatic model for shallow water wave dispersion based on a predictor-corrector scheme. They apply the non-hydrostatic correction only in regions identified as significant by simple indicators rather than solving the elliptic system over the entire domain. The indicators are the ratio of total water depth to surface elevation and the norms of horizontal velocities. Tests with wave trains over a shoal and with static or moving bottom tsunami-like propagation show that accuracy matches the uniform non-hydrostatic version. This selective approach matters for coastal modeling because it lowers the expense of capturing dispersive effects at large scales.

Core claim

The model applies a non-hydrostatic correction to the shallow water equations in a predictor-corrector scheme, but only locally in areas identified by the ratio of total water depth to surface elevation and by horizontal velocity norms. This selective application reduces the computational effort by approximately 40% compared to uniform application while maintaining accuracy in standard test cases including wave trains over a semi-circular shoal and static and moving bottom tsunami-like wave propagation.

What carries the argument

The local adaptation mechanism that selects regions for non-hydrostatic correction based on depth-elevation ratio and velocity norms within a predictor-corrector framework.

If this is right

  • Tsunami propagation models can handle larger domains at the same computational expense.
  • The elliptic solver for corrections runs only on subsets of the grid, lowering overall runtime.
  • Accuracy in dispersive wave effects is preserved in critical areas like shoals.
  • Interface between hydrostatic and non-hydrostatic regions does not introduce significant errors in the tested scenarios.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar local adaptation could apply to three-dimensional or other physics extensions in fluid models.
  • Combining this with mesh refinement might yield even greater efficiency gains in variable-resolution setups.
  • Further tests on highly nonlinear or breaking waves would clarify the limits of the indicators.

Load-bearing premise

The chosen indicators reliably identify all regions where non-hydrostatic effects matter without missing critical areas or introducing interface errors.

What would settle it

A new wave scenario in which the indicators fail to flag a dispersion-critical zone, producing wave heights or phases that deviate from a full non-hydrostatic reference solution.

Figures

Figures reproduced from arXiv: 2606.27562 by J\"orn Behrens, Kemal Firdaus.

Figure 15
Figure 15. Figure 15: The locally adaptive model takes 65.17% and 61.80% of the computational time for the linear and quadratic pressure, respectively. This case reaffirms that tsunami-type waves can benefit from locally adaptive models. FIGURE 14 Absolute difference of the simulated surface elevation between locally adaptive and global model with linear (left) and quadratic (right) pressure relation at the end of simulation t… view at source ↗
read the original abstract

We introduce a two-dimensional non-hydrostatic model for shallow water wave dispersion. The model is based on a locally adapted application of a non-hydrostatic correction to the hydrostatic shallow water equations (SWE) in a predictor-corrector scheme. Applying the non-hydrostatic correction uniformly to the entire domain demands a high computational cost, since an elliptic system of equations needs to be solved for the correction terms. We demonstrate that by determining the area where the non-hydrostatic effects are significant, and applying the correction only locally, the computational effort can be reduced by approximately 40\% without sacrificing accuracy in tsunami-like scenarios. As indicators for the non-hydrostatic effect, we use the ratio between total water depth and surface elevation, as well as horizontal velocity norms. Results are shown for several well-known test cases, including wave trains over a semi-circular shoal, static, and moving bottom tsunami-like wave propagation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a two-dimensional non-hydrostatic extension of the shallow water equations based on a predictor-corrector scheme with locally adaptive application of the elliptic correction. Regions for the non-hydrostatic correction are identified using two heuristic indicators (ratio of total water depth to surface elevation, and horizontal velocity norms), yielding an empirical reduction in computational cost of approximately 40% with no reported loss of accuracy on tsunami-like test cases including wave trains over a semi-circular shoal and static/moving-bottom tsunami generation.

Significance. If the local indicators prove robust, the approach would provide a practical efficiency gain for dispersive shallow-water models in large-domain applications such as tsunami forecasting, where full-domain elliptic solves dominate cost. The work demonstrates the savings empirically on standard benchmarks and credits the underlying non-hydrostatic formulation, offering a concrete step toward scalable non-hydrostatic modeling without requiring new theoretical derivations.

major comments (3)
  1. [Methodology on locally adaptive scheme] Section describing the indicator thresholds: the two indicators are controlled by free thresholds whose values are chosen per test case; no sensitivity study is presented showing that the reported 40% savings and accuracy hold under modest threshold perturbations, which directly bears on whether the local scheme reliably generalizes beyond the presented suite.
  2. [Shoal test case results] Results section on the semi-circular shoal test: the claim of maintained accuracy rests on visual comparison of surface elevation snapshots; quantitative L2 or L-infinity error norms between the locally adaptive solution and the full non-hydrostatic reference solution are not reported, leaving the 'without sacrificing accuracy' assertion unsupported by the data shown.
  3. [Predictor-corrector scheme] Section on the predictor-corrector implementation: no analysis or numerical test addresses continuity of the non-hydrostatic pressure correction or velocity at the dynamic interfaces between hydrostatic and non-hydrostatic cells; abrupt switching could introduce local artifacts not captured by the chosen tsunami-like benchmarks.
minor comments (2)
  1. The abstract and introduction would benefit from an explicit statement of the precise error metric (e.g., relative L2 norm) used to assert 'maintained accuracy'.
  2. Figure captions for the tsunami tests could include the specific threshold values employed for each indicator to aid reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate the revisions that will be incorporated.

read point-by-point responses

  1. Referee: Section describing the indicator thresholds: the two indicators are controlled by free thresholds whose values are chosen per test case; no sensitivity study is presented showing that the reported 40% savings and accuracy hold under modest threshold perturbations, which directly bears on whether the local scheme reliably generalizes beyond the presented suite.

    Authors: The thresholds are selected empirically according to the physical interpretation of the indicators to identify regions of significant dispersion in tsunami-like flows. They are not arbitrary but tuned to the wave characteristics of each benchmark while remaining consistent across the test suite. To strengthen the generalization claim, we will add a sensitivity analysis in the revised manuscript by varying each threshold by ±10% and ±20% on the semi-circular shoal case and reporting the resulting changes in both computational cost and solution fidelity. revision: yes

  2. Referee: Results section on the semi-circular shoal test: the claim of maintained accuracy rests on visual comparison of surface elevation snapshots; quantitative L2 or L-infinity error norms between the locally adaptive solution and the full non-hydrostatic reference solution are not reported, leaving the 'without sacrificing accuracy' assertion unsupported by the data shown.

    Authors: We agree that quantitative norms provide stronger evidence than visual inspection alone. Although the snapshots already indicate close agreement with the full non-hydrostatic reference, we will compute and tabulate L2 and L-infinity norms of surface elevation against the reference solution at representative times in the revised results section. revision: yes

  3. Referee: Section on the predictor-corrector implementation: no analysis or numerical test addresses continuity of the non-hydrostatic pressure correction or velocity at the dynamic interfaces between hydrostatic and non-hydrostatic cells; abrupt switching could introduce local artifacts not captured by the chosen tsunami-like benchmarks.

    Authors: The non-hydrostatic pressure correction is solved only inside the locally marked region and is identically zero outside it; the velocity update is performed uniformly, so the correction field is continuous by construction at the moving interfaces. No spurious artifacts appeared in any of the presented benchmarks. We will add a concise paragraph in the methodology section explaining this interface treatment and its continuity properties. revision: partial

Circularity Check

0 steps flagged

No circularity; local adaptation and savings are empirical outcomes of chosen indicators on test cases

full rationale

The paper introduces a predictor-corrector non-hydrostatic extension to SWE and selects two explicit local indicators (depth-to-elevation ratio and velocity norms) to decide where the elliptic correction is applied. The 40% cost reduction is reported as a measured outcome on standard tsunami and shoal benchmarks after applying those fixed thresholds; no parameter is fitted to the target accuracy metric, no result is renamed as a prediction, and no load-bearing premise rests on self-citation. The central claim therefore remains an independent numerical demonstration rather than a definitional or self-referential reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach relies on standard numerical methods for SWE and a predictor-corrector scheme; the local adaptation is the main addition.

free parameters (1)
  • thresholds for indicators
    The specific cutoffs for when to apply the correction are likely tuned but not detailed in abstract.
axioms (1)
  • domain assumption Standard assumptions of shallow water equations hold in the hydrostatic part.
    The model builds on SWE which assume hydrostatic pressure except where corrected.

pith-pipeline@v0.9.1-grok · 5688 in / 1211 out tokens · 40195 ms · 2026-06-29T00:38:34.789024+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references · 35 canonical work pages

  1. [1]

    Validation and inter-comparison of models for landslide tsunami generation.Ocean Modelling2022; 170: 101943

    Kirby JT, Grilli ST, Horrillo J, et al. Validation and inter-comparison of models for landslide tsunami generation.Ocean Modelling2022; 170: 101943. doi: https://doi.org/10.1016/j.ocemod.2021.101943 14 FIRDAUS and BEHRENS

    work page doi:10.1016/j.ocemod.2021.101943 2021

  2. [2]

    Dispersion of tsunamis: does it really matter?.Natural Hazards and Earth System Sciences2013; 13(6): 1507–1526

    Glimsdal S, Pedersen GK, Harbitz CB, Løvholt F. Dispersion of tsunamis: does it really matter?.Natural Hazards and Earth System Sciences2013; 13(6): 1507–1526. doi: 10.5194/nhess-13-1507-2013

    work page doi:10.5194/nhess-13-1507-2013 2013

  3. [3]

    Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model.Coastal Engineering2010; 57(9): 779-794

    Abadie S, Morichon D, Grilli S, Glockner S. Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model.Coastal Engineering2010; 57(9): 779-794. doi: https://doi.org/10.1016/j.coastaleng.2010.03.003

    work page doi:10.1016/j.coastaleng.2010.03.003 2010

  4. [4]

    doi: https://doi.org/10.1016/j.apm.2021.02.014

    AiC,MaY,YuanC,XieZ,DongG.Athree-dimensionalnon-hydrostaticmodelfortsunamiwavesgeneratedbysubmarine landslides.Applied Mathematical Modelling2021; 96: 1-19. doi: https://doi.org/10.1016/j.apm.2021.02.014

    work page doi:10.1016/j.apm.2021.02.014 2021

  5. [5]

    Numerical modeling of submarine mass-movement generated waves using RANS model.Com- puters & Geosciences2006; 32(7): 927-935

    Yuk D, Yim S, Liu PF. Numerical modeling of submarine mass-movement generated waves using RANS model.Com- puters & Geosciences2006; 32(7): 927-935. Computer Simulation of natural phenomena for Hazard Assessmentdoi: https://doi.org/10.1016/j.cageo.2005.10.028

    work page doi:10.1016/j.cageo.2005.10.028 2005

  6. [6]

    Higher–order Boussinesq–type equations for surface gravity waves: derivation and analysis

    Madsen PA, Schäffer HA. Higher–order Boussinesq–type equations for surface gravity waves: derivation and analysis. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 1998; 356(1749): 3123-3181. doi: 10.1098/rsta.1998.0309

    work page doi:10.1098/rsta.1998.0309 1998

  7. [7]

    Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis.Proceedings of the Royal Society of London

    Madsen PA, Bingham HB, Schäffer HA. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis.Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences2003; 459(2033): 1075-1104. doi: 10.1098/rspa.2002.1067

    work page doi:10.1098/rspa.2002.1067 2033

  8. [8]

    doi: https://doi.org/10.1016/j.coastaleng.2005.11.002

    MadsenPA,FuhrmanDR,WangB.ABoussinesq-typemethodforfullynonlinearwavesinteractingwitharapidlyvarying bathymetry.Coastal Engineering2006; 53(5): 487-504. doi: https://doi.org/10.1016/j.coastaleng.2005.11.002

    work page doi:10.1016/j.coastaleng.2005.11.002 2005

  9. [9]

    Tsunami generation, propagation, and run-up with a high-order Boussinesq model.Coastal Engineering2009; 56(7): 747-758

    Fuhrman DR, Madsen PA. Tsunami generation, propagation, and run-up with a high-order Boussinesq model.Coastal Engineering2009; 56(7): 747-758. doi: 10.1016/j.coastaleng.2009.02.004

    work page doi:10.1016/j.coastaleng.2009.02.004 2009

  10. [10]

    Development and validation of a two-layer Boussinesq model for simulating free surface waves generated by bottom motion.Applied Ocean Research2020; 94: 101977

    Fang K, Liu Z, Sun J, Xie Z, Zheng Z. Development and validation of a two-layer Boussinesq model for simulating free surface waves generated by bottom motion.Applied Ocean Research2020; 94: 101977. doi: https://doi.org/10.1016/j.apor.2019.101977

    work page doi:10.1016/j.apor.2019.101977 2019

  11. [11]

    Boussinesq modeling of surface waves due to underwater landslides.Nonlinear Processes in Geophysics2013; 20(3): 267–285

    Dutykh D, Kalisch H. Boussinesq modeling of surface waves due to underwater landslides.Nonlinear Processes in Geophysics2013; 20(3): 267–285. doi: 10.5194/npg-20-267-2013

    work page doi:10.5194/npg-20-267-2013 2013

  12. [12]

    Stelling G, Zijlema M. An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation.International Journal for Numerical Methods in Fluids2003; 43(1): 1-23. doi: 10.1002/fld.595

    work page doi:10.1002/fld.595

  13. [13]

    doi: https://doi.org/10.1002/fld.1019

    WaltersRA.Asemi-implicitfiniteelementmodelfornon-hydrostatic(dispersive)surfacewaves.International Journal for Numerical Methods in Fluids2005; 49(7): 721-737. doi: https://doi.org/10.1002/fld.1019

    work page doi:10.1002/fld.1019

  14. [14]

    doi: 10.1002/fld.1952

    YamazakiY,KowalikZ,CheungKF.Depth-integrated,non-hydrostaticmodelforwavebreakingandrun-up.International Journal for Numerical Methods in Fluids2009; 61(5): 473-497. doi: 10.1002/fld.1952

    work page doi:10.1002/fld.1952 1952

  15. [15]

    Jeschke A, Pedersen GK, Vater S, Behrens J. Depth-averaged non-hydrostatic extension for shallow water equations with quadraticverticalpressureprofile:equivalencetoBoussinesq-typeequations.International Journal for Numerical Methods in Fluids2017; 84(10): 569-583. doi: 10.1002/fld.4361

    work page doi:10.1002/fld.4361

  16. [16]

    An improved depth-averaged nonhydrostatic shallow water model with quadratic pressure approximation.International Journal for Numerical Methods in Fluids2020; 92(8): 803-824

    Wang W, Martin T, Kamath A, Bihs H. An improved depth-averaged nonhydrostatic shallow water model with quadratic pressure approximation.International Journal for Numerical Methods in Fluids2020; 92(8): 803-824. doi: 10.1002/fld.4807

    work page doi:10.1002/fld.4807

  17. [17]

    Hydrodynamic coupling of multi-fidelity solvers in REEF3D with application to ship-induced wave modelling.Coastal Engineering2024; 188: 104452

    Dempwolff LC, Windt C, Bihs H, Melling G, Holzwarth I, Goseberg N. Hydrodynamic coupling of multi-fidelity solvers in REEF3D with application to ship-induced wave modelling.Coastal Engineering2024; 188: 104452. doi: 10.1016/j.coastaleng.2023.104452

    work page doi:10.1016/j.coastaleng.2023.104452 2023

  18. [18]

    A derivation of equations for wave propagation in water of variable depth.Journal of Fluid Mechanics1976; 78(2): 237–246

    Green AE, Naghdi PM. A derivation of equations for wave propagation in water of variable depth.Journal of Fluid Mechanics1976; 78(2): 237–246. doi: 10.1017/S0022112076002425 FIRDAUS and BEHRENS 15

    work page doi:10.1017/s0022112076002425

  19. [19]

    Locally Adaptive Non-Hydrostatic Shallow Water Extension for Moving Bottom-Generated Waves

    Firdaus K, Behrens J. Locally Adaptive Non-Hydrostatic Shallow Water Extension for Moving Bottom-Generated Waves. International Journal for Numerical Methods in Fluids2026; 98(2): 159-173. doi: https://doi.org/10.1002/fld.70021

    work page doi:10.1002/fld.70021

  20. [20]

    Firdaus K, Behrens J. Non-Hydrostatic Model for Simulating Moving Bottom-Generated Waves: A Shallow Water Exten- sion With Quadratic Vertical Pressure Profile.International Journal for Numerical Methods in Fluids2025; 97(8): 1093-1103. doi: https://doi.org/10.1002/fld.5393

    work page doi:10.1002/fld.5393

  21. [21]

    Optimal dispersion with minimized Poisson equations for non-hydrostatic free surface flows

    Cui H, Pietrzak J, Stelling G. Optimal dispersion with minimized Poisson equations for non-hydrostatic free surface flows. Ocean Modelling2014; 81: 1-12. doi: https://doi.org/10.1016/j.ocemod.2014.06.004

    work page doi:10.1016/j.ocemod.2014.06.004 2014

  22. [22]

    A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows.Journal of Computational Physics2020; 418: 109609

    Popinet S. A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows.Journal of Computational Physics2020; 418: 109609. doi: https://doi.org/10.1016/j.jcp.2020.109609

    work page doi:10.1016/j.jcp.2020.109609 2020

  23. [23]

    An Efficient Two-Layer Non-Hydrostatic Model for Investigating Wave Run-Up Phenomena

    Magdalena I, Erwina N. An Efficient Two-Layer Non-Hydrostatic Model for Investigating Wave Run-Up Phenomena. Computation2020; 8(1). doi: 10.3390/computation8010001

    work page doi:10.3390/computation8010001

  24. [24]

    doi: https://doi.org/10.1002/fld.4762

    VaterS,BeisiegelN,BehrensJ.Alimiter-basedwell-balanceddiscontinuousGalerkinmethodforshallow-waterflowswith wetting and drying: Triangular grids.International Journal for Numerical Methods in Fluids2019; 91(8): 395-418. doi: https://doi.org/10.1002/fld.4762

    work page doi:10.1002/fld.4762

  25. [25]

    The calculation of the interaction of non-stationary shock waves and obstacles.USSR Computational Mathematics and Mathematical Physics1962; 1(2): 304-320

    Rusanov V. The calculation of the interaction of non-stationary shock waves and obstacles.USSR Computational Mathematics and Mathematical Physics1962; 1(2): 304-320. doi: https://doi.org/10.1016/0041-5553(62)90062-9

    work page doi:10.1016/0041-5553(62)90062-9

  26. [26]

    A high-order triangular discontinuous Galerkin oceanic shallow water model.International Journal for Numerical Methods in Fluids2008; 56(7): 899-925

    Giraldo FX, Warburton T. A high-order triangular discontinuous Galerkin oceanic shallow water model.International Journal for Numerical Methods in Fluids2008; 56(7): 899-925. doi: 10.1002/fld.1562

    work page doi:10.1002/fld.1562

  27. [27]

    Texts in Applied MathematicsSpringer New York, NY

    Hesthaven JS, Warburton T.Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Texts in Applied MathematicsSpringer New York, NY. 1 ed. 2008

    2008

  28. [28]

    A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics.Journal of Computational Physics2021; 442: 110467

    Schlottke-Lakemper M, Winters AR, Ranocha H, Gassner GJ. A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics.Journal of Computational Physics2021; 442: 110467. doi: https://doi.org/10.1016/j.jcp.2021.110467

    work page doi:10.1016/j.jcp.2021.110467 2021

  29. [29]

    Texts in Computational Science and Engineering (TCSE, Volume 24)Springer Cham

    Giraldo FX.An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases: Analysis, Algorithms, and Applications. Texts in Computational Science and Engineering (TCSE, Volume 24)Springer Cham . 2020

    2020

  30. [30]

    The Limit of Applicability of Linear Wave Refraction Theory in a Convergence Zone

    Whalin RW. The Limit of Applicability of Linear Wave Refraction Theory in a Convergence Zone. research report h-71-3, U.S. Army Corps of Engineers, Waterways Experiment Station; Vicksburg, MS, USA: 1971. Hydraulics Laboratory

    1971

  31. [31]

    doi:https://doi.org/10.1016/0378-3839(92)90019- Q

    MadsenPA,SørensenOR.AnewformoftheBoussinesqequationswithimprovedlineardispersioncharacteristics.Part2.A slowly-varyingbathymetry.Coastal Engineering1992;18(3):183-204. doi:https://doi.org/10.1016/0378-3839(92)90019- Q

    work page doi:10.1016/0378-3839(92)90019-

  32. [32]

    doi: https://doi.org/10.1016/j.coastaleng.2012.05.008

    KazoleaM,DelisA,NikolosI,SynolakisC.Anunstructuredfinitevolumenumericalschemeforextended2DBoussinesq- type equations.Coastal Engineering2012; 69: 42-66. doi: https://doi.org/10.1016/j.coastaleng.2012.05.008

    work page doi:10.1016/j.coastaleng.2012.05.008 2012

  33. [33]

    A new class of fully nonlinear and weakly dispersive Green–Naghdi models for efficient 2D simulations.Journal of Computational Physics2015; 282: 238-268

    Lannes D, Marche F. A new class of fully nonlinear and weakly dispersive Green–Naghdi models for efficient 2D simulations.Journal of Computational Physics2015; 282: 238-268. doi: https://doi.org/10.1016/j.jcp.2014.11.016

    work page doi:10.1016/j.jcp.2014.11.016 2014

  34. [34]

    doi: 10.1007/BF00874384

    BriggsMJ,SynolakisCE,HarkinsGS,GreenDR.Laboratoryexperimentsoftsunamirunuponacircularisland.Pure and Applied Geophysics1995; 144(3): 569–593. doi: 10.1007/BF00874384

    work page doi:10.1007/bf00874384

  35. [35]

    Runup of solitary waves on a circular Island.Journal of Fluid Mechanics1995; 302: 259–285

    Liu PLF, Cho YS, Briggs MJ, Kanoglu U, Synolakis CE. Runup of solitary waves on a circular Island.Journal of Fluid Mechanics1995; 302: 259–285. doi: 10.1017/S0022112095004095

    work page doi:10.1017/s0022112095004095

  36. [36]

    Experimental Study of Tsunami Generation by Three-Dimensional Rigid Underwater Landslides

    Enet F, Grilli ST. Experimental Study of Tsunami Generation by Three-Dimensional Rigid Underwater Landslides. Journal of Waterway, Port, Coastal, and Ocean Engineering2007; 133(6): 442-454. doi: 10.1061/(ASCE)0733- 950X(2007)133:6(442) 16 FIRDAUS and BEHRENS

    work page doi:10.1061/(asce)0733- 2007

  37. [37]

    Multilayer-HySEA model validation for landslide-generated tsunamis – Part 1: Rigid slides.Natural Hazards and Earth System Sciences2021; 21(2): 775–789

    Macías J, Escalante C, Castro MJ. Multilayer-HySEA model validation for landslide-generated tsunamis – Part 1: Rigid slides.Natural Hazards and Earth System Sciences2021; 21(2): 775–789. doi: 10.5194/nhess-21-775-2021

    work page doi:10.5194/nhess-21-775-2021 2021

  38. [38]

    An efficient two-dimensional non-hydrostatic model for simulating submarine landslide-generated tsunamis.Ocean Engineering2024; 310: 118750

    Tarwidi D, Pudjaprasetya SR, Adytia D, Subasita N. An efficient two-dimensional non-hydrostatic model for simulating submarine landslide-generated tsunamis.Ocean Engineering2024; 310: 118750. doi: https://doi.org/10.1016/j.oceaneng.2024.118750

    work page doi:10.1016/j.oceaneng.2024.118750 2024

  39. [39]

    The NTHMP Landslide Tsunami Benchmark Workshop, Galveston, Texas, USA, 9–11 January 2017

    Kirby J, Grilli S, Zhang C, Horrillo J, Nicolsky D, Liu PLF. The NTHMP Landslide Tsunami Benchmark Workshop, Galveston, Texas, USA, 9–11 January 2017. tech. rep., Research Report CACR-18-01; Newark, Delaware, USA: 2018. Tech. Rep

    2017