A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave Simulation
A new three-dimensional high-order shock-capturing model for the numerical simulation of breaking waves is proposed. The proposed model is based on an integral contravariant form of the Navier–Stokes equations in a time-dependent generalized curvilinear coordinate system. Such an integral contravari...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Journal of Marine Science and Engineering |
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| Online Access: | https://www.mdpi.com/2077-1312/10/6/810 |
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| author | Giovanni Cannata Federica Palleschi Benedetta Iele Francesco Gallerano |
| author_facet | Giovanni Cannata Federica Palleschi Benedetta Iele Francesco Gallerano |
| author_sort | Giovanni Cannata |
| collection | DOAJ |
| description | A new three-dimensional high-order shock-capturing model for the numerical simulation of breaking waves is proposed. The proposed model is based on an integral contravariant form of the Navier–Stokes equations in a time-dependent generalized curvilinear coordinate system. Such an integral contravariant form of the equations of motion is numerically integrated by a new conservative numerical scheme that is based on three elements of originality: the time evolution of the state of the system is carried out using a predictor–corrector method in which exclusively the conserved variables are used; the point values of the conserved variables on the cell face of the computational grid are obtained using an original high-order reconstruction procedure called a wave-targeted essentially non-oscillatory scheme; the time evolution of the discontinuity on the cell faces is calculated using an exact Riemann solver. The proposed model is validated by numerically reproducing several experimental tests of breaking waves on computational grids that are significantly coarser than those used in the literature to validate the existing 3D shock-capturing models. The results obtained with the proposed model are also compared with those obtained with a previously published model, which is based on second-order total variation diminishing reconstructions and an approximate Riemann solver usually adopted in the existing 3D shock-capturing models. Through the above comparison, the main drawbacks of the existing 3D shock-capturing models and the ability of the proposed model to simulate breaking waves and wave-induced currents are shown. The proposed 3D model is able to correctly simulate the wave height increase in the shoaling zone and to effectively predict the location of the wave breaking point, the maximum wave height, and the wave height decay in the surf zone. The validated model is applied to the simulation of the interaction between breaking waves and an emerged breakwater. The numerical results show that the proposed model is able to simulate both the large-scale circulation patterns downstream of the barrier and the onset of quasi-periodic vortex structures close to the edge of the barrier. |
| first_indexed | 2024-03-09T23:23:47Z |
| format | Article |
| id | doaj.art-d0a0177deff64fca913136143b5114e3 |
| institution | Directory Open Access Journal |
| issn | 2077-1312 |
| language | English |
| last_indexed | 2024-03-09T23:23:47Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Marine Science and Engineering |
| spelling | doaj.art-d0a0177deff64fca913136143b5114e32023-11-23T17:23:17ZengMDPI AGJournal of Marine Science and Engineering2077-13122022-06-0110681010.3390/jmse10060810A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave SimulationGiovanni Cannata0Federica Palleschi1Benedetta Iele2Francesco Gallerano3Department of Civil, Constructional and Environmental Engineering, Sapienza University of Rome, 00184 Rome, ItalyDepartment of Civil, Constructional and Environmental Engineering, Sapienza University of Rome, 00184 Rome, ItalyDepartment of Civil, Constructional and Environmental Engineering, Sapienza University of Rome, 00184 Rome, ItalyDepartment of Civil, Constructional and Environmental Engineering, Sapienza University of Rome, 00184 Rome, ItalyA new three-dimensional high-order shock-capturing model for the numerical simulation of breaking waves is proposed. The proposed model is based on an integral contravariant form of the Navier–Stokes equations in a time-dependent generalized curvilinear coordinate system. Such an integral contravariant form of the equations of motion is numerically integrated by a new conservative numerical scheme that is based on three elements of originality: the time evolution of the state of the system is carried out using a predictor–corrector method in which exclusively the conserved variables are used; the point values of the conserved variables on the cell face of the computational grid are obtained using an original high-order reconstruction procedure called a wave-targeted essentially non-oscillatory scheme; the time evolution of the discontinuity on the cell faces is calculated using an exact Riemann solver. The proposed model is validated by numerically reproducing several experimental tests of breaking waves on computational grids that are significantly coarser than those used in the literature to validate the existing 3D shock-capturing models. The results obtained with the proposed model are also compared with those obtained with a previously published model, which is based on second-order total variation diminishing reconstructions and an approximate Riemann solver usually adopted in the existing 3D shock-capturing models. Through the above comparison, the main drawbacks of the existing 3D shock-capturing models and the ability of the proposed model to simulate breaking waves and wave-induced currents are shown. The proposed 3D model is able to correctly simulate the wave height increase in the shoaling zone and to effectively predict the location of the wave breaking point, the maximum wave height, and the wave height decay in the surf zone. The validated model is applied to the simulation of the interaction between breaking waves and an emerged breakwater. The numerical results show that the proposed model is able to simulate both the large-scale circulation patterns downstream of the barrier and the onset of quasi-periodic vortex structures close to the edge of the barrier.https://www.mdpi.com/2077-1312/10/6/810three-dimensional modelwave breakingconservative schemehigh-order reconstructionsexact Riemann solvercontravariant formulation |
| spellingShingle | Giovanni Cannata Federica Palleschi Benedetta Iele Francesco Gallerano A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave Simulation Journal of Marine Science and Engineering three-dimensional model wave breaking conservative scheme high-order reconstructions exact Riemann solver contravariant formulation |
| title | A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave Simulation |
| title_full | A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave Simulation |
| title_fullStr | A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave Simulation |
| title_full_unstemmed | A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave Simulation |
| title_short | A Wave-Targeted Essentially Non-Oscillatory 3D Shock-Capturing Scheme for Breaking Wave Simulation |
| title_sort | wave targeted essentially non oscillatory 3d shock capturing scheme for breaking wave simulation |
| topic | three-dimensional model wave breaking conservative scheme high-order reconstructions exact Riemann solver contravariant formulation |
| url | https://www.mdpi.com/2077-1312/10/6/810 |
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