A High-order Pseudospectral Incompressible Navier-Stokes Free Surface Model in 2D

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Abstract

Simulation of water waves and taking into account the sea floor to estimate sea states areimportant for the design of offshore structures. We propose a new high-order accurate pseudospectral method for solving the incompressible Navier-Stokes equations with a free surface.The work is motivated by the lack of high-order accurate free surface water wave models whichinclude viscous and rotational effects. The numerical scheme utilizes Fourier and Chebyshevbasis functions for the numerical discretization and enables exploiting the fast Fourier transform (FFT) algorithm for efficiency reasons. A key feature is an explicit-implicit pressure-correctionmethod designed to work with general Runge-Kutta (RK) methods used for temporal integration that fulfills mass balance and a pressure-velocity coupling. Another key feature is the useof a Fourier-continuation technique for solving numerical wave tank problems on finite (nonperiodic) domains. As a starting point towards establishing the solver, we provide benchmarkresults to demonstrate accuracy and convergence using established cases used for potential flowsolvers. We present numerical case results for i) nonlinear stream function wave solutions and ii) steep solitary wave reflection in a numerical wave tank in this abstract.
Original languageEnglish
Publication date2022
Number of pages4
Publication statusPublished - 2022
Event37th International Workshop on Water Waves and Floating Bodies - Una Hotel, Giardini Naxos, Italy
Duration: 10 Apr 202213 Apr 2022

Conference

Conference37th International Workshop on Water Waves and Floating Bodies
LocationUna Hotel
Country/TerritoryItaly
CityGiardini Naxos
Period10/04/202213/04/2022

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