Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup
Abstract
:1. Introduction
2. Description of the Model
2.1. Governing Equations
2.2. Numerical Formulation
2.2.1. First Step: Discontinuous Galerkin Solution
2.2.2. New Slope Limiter
2.2.3. Second Step: Continuous Galerkin Solution
2.2.4. Third Step
2.2.5. Boundary Conditions
2.2.6. Dry Bed Treatment
2.2.7. Wave Breaking
- The surface variation criterion: a node is flagged if , with ∈ [0.3, 0.65] depending on the type of breaker.
- The local slope angle criterion: a node is flagged if ≥ tan ϕ, with ϕ ∈ [14°, 33°] depending on the flow configuration.
2.2.8. Computational Aspects
3. Model Verification and Validation
3.1. Solitary Wave Propagation Along a Constant Depth Channel
3.2. Solitary Wave Runup on a Plane Beach
3.3. Solitary Wave Propagation over Fringing Reef
3.4. Series of Regular Waves on a Plane Beach
3.5. Solitary Wave Runup on a Conical Island
3.6. Solitary Wave Transformation, Breaking and Runup over a Three-Dimensional Complex Bathymetry.
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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T (sec) | h (m) | Breaking Type | ||||
---|---|---|---|---|---|---|
T1 | 11 | 2 | 4.62 | 0.70 | 0.37 | Spilling |
T2 | 6.5 | 4 | 10.12 | 0.70 | 0.74 | Plunging |
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Calvo, L.; De Padova, D.; Mossa, M.; Rosman, P. Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup. Computation 2021, 9, 47. https://doi.org/10.3390/computation9040047
Calvo L, De Padova D, Mossa M, Rosman P. Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup. Computation. 2021; 9(4):47. https://doi.org/10.3390/computation9040047
Chicago/Turabian StyleCalvo, Lucas, Diana De Padova, Michele Mossa, and Paulo Rosman. 2021. "Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup" Computation 9, no. 4: 47. https://doi.org/10.3390/computation9040047