Compensation of the Afterglow Phenomenon in 2-D Discrete-Time Simulations

Due to high computational costs, the physics governed by the wave equation in 3-D is often modelled via discrete-time numerical simulations conducted in 2-D scenarios. Results are normally generalized to 3-D rather straightforwardly, overlooking the fact that the propagation of a point-like impulse in 2-D exhibits the so-called afterglow phenomenon, which consists on the fact that non-null field values are measured after the arrival of the first wavefront. This letter analyzes the consequences of this phenomenon, both theoretically and numerically, and presents a simple method to compensate for it. Verification of this method is presented using various discrete-time numerical schemes.