Simulation of wave propagation with obstacles: Time invariance operator applied to interference and diffraction

Abstract

We present here a computational numerical operator, and we name it as Time Invariance Operator (TIO). This operator can add obstacles to the domain of the differential equation that describes a physical phenomenon. After the TIO acts, the wave equation recognizes the introduced points as non-interacting zones without affecting the rest of the domain. Computational physics has been consolidated as an important field of study, especially when connected with the fundamentals of physics. In many cases, simulations are conducted considering the ideal case of a wave in an infinite domain and open space without considering obstacles, barriers, or other aspects of the real world. The results presented in this paper allow us to infer that the TIO is the easiest way to apply the physical domain to wave propagation simulations and successfully recreate wave interaction experiments through computer simulations. Our motivation is to perform wave simulations that interact with obstacles, barriers, single slits, and double slits. We aim to investigate the results obtained in images to determine if the methodology we used to introduce realistic physical characteristics was successful in presenting the expected phenomenology. The simplicity of the TIO’s action in creating locally time-invariant regions over the domain makes it suitable not only for waves but also for equations with transient terms. Heat transfer, mass transfer, computational fluid dynamics, and other time evolution equations can take some benefit from the operator presented in this paper. The TIO ensures local conservation that mimics interaction regions or ensures free space characteristics if it is the case like a 2D tensor of local conservation. The principal result from this paper is the validation of the TIO to impose realistic conditions with minimal modifications over a running code of wave equation simulation originally in free space. The TIO is innovative because it imposes dynamic conditions that mimic realistic interacting zones.