Implicit Chebyshev spectral element method for acoustics wave equations

In the present study, the Chebyshev spectral element method coupled with the implicit Newmark time integral method is investigated to simulate acoustic field. The approach is first applied to a numerical example. In this case, the numerical result is consistent with the reference solution, and the influence of time step and Newmark factor on numerical accuracy is studied. The resulting figures indicate that the smaller the time step and Newmark factor are, the higher the numerical accuracy will be. The division pattern of computational domain can affect the numerical accuracy, which indicates that the numerical accuracy can be improved when the grid nodes tend to be distributed uniformly in the computational domain. Secondly, a numerical example is used to investigate the absorbing boundary condition, the result of which indicates that the absorbing boundary condition absorbs the numerical reflection whereas the Dirichlet boundary condition causes the numerical reflection. Moreover, the approach is also employed for wave equation with source terms such as monopole, dipole and quadrapole, whose numerical results keep their radiation traits intactly.