Explicit finite-difference method with time-step n-tupling and extended CFL stability limit for acoustic wave...

The explicit finite-difference scheme is widely used in seismic wave simulation. Using large time steps can significantly reduce the number of iterations and thus improve computational efficiency, but this approach faces two main challenges: reduced accuracy caused by temporal dispersion and restrictions imposed by the Courant-Friedrichs-Lewy (CFL) stability condition. Based on the wavefield iteration equation in matrix form, an explicit finite-difference method with time step n-tupling and an extended CFL limit is developed for acoustic wave simulation. By combining n successive iteration operators into a single-step operator, two types of n-tupling algorithms are constructed, effectively expanding the CFL stability limit by a factor of n and enabling time steps well beyond conventional thresholds. Both theoretical analysis and numerical experiments demonstrate that simulations with time step n-tupling achieve accuracy equivalent to conventional single-step methods while reducing computation time to approximately 1/n, resulting in a corresponding n-fold increase in overall computational efficiency. Time dispersion is suppressed using two complementary strategies: for relatively small base time steps, n-tupling inherently attains the accuracy of smaller steps; for relatively large base steps, a time-dispersion transform is applied to eliminate errors and maintain high numerical accuracy throughout the simulation.