quadratic finite element method for numerical solution of underwater wave propagation

In this paper, sound propagation in shallow water environments is studied. a quadratic finite element method (qfem)‎ by means of functional technique in conjunction with narrow angle parabolic model of hyperbolic wave equation is applied by solving wave equation in depth dependent and range independent fluid-solid media. the capability of fem based method for modeling of complex solid-fluid boundaries in bottom and also the random surface is employed for formulating of depth operators in parabolic equation (pe)‎ method. after simplifying of some integrals in qfem, the governing system of equations are obtained. due to existence of mass matrix in the final system, implicit methods seem to be reliable tools for solving such algebraic system of equations that here, crank-nicolson approach is used for estimation of solution. checking of proposed method efficiency is determined by some standard test problems. the obtained results show acceptable agreement with the physical behavior of wave propagation nature but for finding of more accurate and capable methods, it requires to develop this method for wide angle pe in associated with more numerical tricks especially in bottom interfaces.