Generalized finite difference time domain simulation on acoustical moving boundary problems

Mesh-free methods have the potential to solve acoustic problems with moving boundary, complex geometries and in flowing fluids. In this paper, generalized finite difference time domain (GFDTD), a time-domain representation of the generalized finite different method (GFDM), is extended to solve acoustic wave problems with moving boundary. To explore the numerical performance of GFDTD, its stability and phase velocity for wave propagations are firstly analyzed by von Neumann method. Compared with the other two widely used mesh-free methods, smoothed particle hydrodynamics (SPH) and modified smoothed particle hydrodynamics (MSPH), theoretical analysis shows that GFDTD has less dispersion, which is also well verified by 1D numerical tests. The GFDTD method is then applied to simulate wave propagation inside a 2D cylinder and the results are compared with those obtained by traditional finite difference time domain (FDTD) method. Finally, a moving boundary condition is introduced into the problem domain and the corresponding input impedance is analyzed.