In this contribution, we present preliminary results of a model for the simulation of three dimensional unsteady nonlinear water waves generated by a ship hull advancing in calm water, under development at the MathLab laboratory of the International School for Advanced Studies of Trieste, Italy. In the framework of potential flow theory, the governing equation is the Laplace's equation, complemented by fully nonlinear free surface boundary conditions. To prevent downstream transport of the mesh nodes and avoid remeshing, such boundary conditions are written in semi-Lagrangian formulation. The resulting boundary value problem is treated as a system of nonlinear differential-algebraic equations, in which the unknowns are the positions of the nodes of the computational grid, along with the corresponding potential and potential normal derivative values. Among these, only vertical positions and potential values associated with free surface nodes, are differential components, as their time evolution is prescribed by ODEs derived from the semi-Lagrangian free surface boundary conditions. All other unknowns are instead algebraic components, their values satisfying algebraic equations resulting from the BEM discretization of the Laplace's equation. The time advancing of nonlinear differential-algebraic system is performed by means of a Backward Differentiation Formula implicit method with variable step size and variable order, implemented in the framework of the open source library Sundials. The collocated and iso-parametric BEM discretization of the Laplace's equation has been implemented employing the open source library deal.II. The semi-Lagrangian free surface boundary conditions are stabilized by means of a Streamwise Upwind Petrov--Galerkin (SUPG) method. The unstructured quadrilateral grids needed for the simulations, are automatically generated on arbitrary CAD hull geometries. The test cases considered are that of a Wigley hull and the US Navy Combatant, DTMB 5415, advancing in calm water. The simulations results obtained are compared with experimental results.

A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves / De Simone, Antonio; Heltai, Luca; Mola, Andrea. - (2012), pp. 1-9. (Intervento presentato al convegno NAV 2012 17th International Conference on Ships and Shipping Research nel October 17, 2012 – October 19, 2012).

### A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves

#### Abstract

In this contribution, we present preliminary results of a model for the simulation of three dimensional unsteady nonlinear water waves generated by a ship hull advancing in calm water, under development at the MathLab laboratory of the International School for Advanced Studies of Trieste, Italy. In the framework of potential flow theory, the governing equation is the Laplace's equation, complemented by fully nonlinear free surface boundary conditions. To prevent downstream transport of the mesh nodes and avoid remeshing, such boundary conditions are written in semi-Lagrangian formulation. The resulting boundary value problem is treated as a system of nonlinear differential-algebraic equations, in which the unknowns are the positions of the nodes of the computational grid, along with the corresponding potential and potential normal derivative values. Among these, only vertical positions and potential values associated with free surface nodes, are differential components, as their time evolution is prescribed by ODEs derived from the semi-Lagrangian free surface boundary conditions. All other unknowns are instead algebraic components, their values satisfying algebraic equations resulting from the BEM discretization of the Laplace's equation. The time advancing of nonlinear differential-algebraic system is performed by means of a Backward Differentiation Formula implicit method with variable step size and variable order, implemented in the framework of the open source library Sundials. The collocated and iso-parametric BEM discretization of the Laplace's equation has been implemented employing the open source library deal.II. The semi-Lagrangian free surface boundary conditions are stabilized by means of a Streamwise Upwind Petrov--Galerkin (SUPG) method. The unstructured quadrilateral grids needed for the simulations, are automatically generated on arbitrary CAD hull geometries. The test cases considered are that of a Wigley hull and the US Navy Combatant, DTMB 5415, advancing in calm water. The simulations results obtained are compared with experimental results.
##### Scheda breve Scheda completa Scheda completa (DC)
2012
NAV 2012 17th International Conference on Ships and Shipping Research
1
9
Associazione Italiana di Tecnica Navale
De Simone, Antonio; Heltai, Luca; Mola, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.11767/15453`
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