Simulation of two-dimensional internal waves generated by a translating and pitching foil

A code developed on the basis of the flux-difference splitting scheme and the hybrid Cartesian/immersed boundary method is applied for two-dimensional simulation of internal waves generated by a foil that is translating and pitching simultaneously near a material interface. The interface is captured as a moving contact discontinuity without any additional treatment along the interface. An approximate Riemann solver is used to estimate numerical fluxes across the discontinuity. Immersed boundary nodes are distributed within an instantaneous fluid domain on the basis of edges crossing a boundary. Dependent variables are reconstructed at the immersed boundary nodes along local normal lines to the boundary. The present results on the propagation of internal solitary waves generated by the collapse mechanism are compared with other computational results and good agreement is found. The code is validated through comparisons with recent experimental results on the waveform inversion from depression type to elevation type during the interaction between an internal solitary wave and a trapezoidal obstacle. Internal waves generated by a translating and pitching foil are simulated. Grid independence tests of the computed results are carried out. Pairs of traveling vortices are correlated to local sinking or rising at the interface.