Generalized Finite Difference Time Domain Method and Its Application to Acoustics

A meshless generalized finite difference time domain (GFDTD) method is proposed and applied to transient acoustics to overcome difficulties due to use of grids or mesh. Inspired by the derivation of meshless particle methods, the generalized finite difference method (GFDM) is reformulated utilizing Taylor series expansion. It is in a way different from the conventional derivation of GFDM in which a weighted energy norm was minimized. The similarity and difference between GFDM and particle methods are hence conveniently examined. It is shown that GFDM has better performance than the modified smoothed particle method in approximating the first- and second-order derivatives of 1D and 2D functions. To solve acoustic wave propagation problems, GFDM is used to approximate the spatial derivatives and the leap-frog scheme is used for time integration. By analog with FDTD, the whole algorithm is referred to as GFDTD. Examples in one- and two-dimensional domain with reflection and absorbing boundary conditions are solved and good agreements with the FDTD reference solutions are observed, even with irregular point distribution. The developed GFDTD method has advantages in solving wave propagation in domain with irregular and moving boundaries.