Investigation of grid convergence in hydroacoustic signal simulation problem in the COMSOL Multiphysics

Hydroacoustic research is inextricably linked to the radiation and registration of acoustic waves. At the same time, the numerical and field modeling of the acoustic wave propagation in water are important research tools. The solution of numerical modeling problems is realized with the use of specialized software packages. As a result, the ability to simulate a problem depends on the technical characteristics of the computer and on the software environment used in the numerical experiment. The mathematical apparatus and software implementation of the model cannot take into account all the variety of factors of real material objects. Therefore, the adequacy of modeling results is a key factor in the applicability of the model. The paper simulates the generation and propagation of an acoustic wave with a frequency of 1 MHz and a duration of 3 periods in water in the COMSOL Multiphysics 6.1 software environment using the finite element method. The criteria for the adequacy of the model were determined; according to them it can be assumed that the results obtained during modeling do not contradict the physical concepts of the ongoing process. For the simulated process, the grid convergence was investigated for the cases with N from 5 to 80, where N is the number of grid cells per wavelength. The simulation radius R varied from 0.02 m to 0.08 m. The following has been analyzed: the time dependences of acoustic pressure at the selected point; the amount of time required to calculate the model at N=20 (R=0.02÷0.08 m); the total number of cells in the generated grid (n) at N=20 (R=0.02÷0.08 m); the effect of the grid thickening on the calculation time of the model (R=0.02 m). The studies have shown that choosing the maximum mesh cell size equal to 1/40 of the wavelength (37.5 μm) for the preset mesh configuration in the Mesh node leads to a reliable result (according to the selected criteria). Based on the results of the work, it is concluded that the technical characteristics of the computer used for modeling make it possible to conduct a numerical experiment on modeling an acoustic wave using a grid with N=40 in a sphere with water with a radius of R=0.04 m.