2D nonlinear Acoustic Wave equation in heterogeneous fluid

Resumo

In this work, the non-linear equation of Acoustic Wave propagation in a heterogeneous fluid (CHACALTANA et al., 2015; PERES et. al., 2023) is solved in two dimensions by Finite Element Method (FEM). The Weighted Residual Method (Petrov-Galerkin) and linear and parabolic approximation basis functions are used to minimize the residue in each element. Ricker-type pressure source (CHACALTANA et al., 2015; PICOLLI et al., 2020) and the sinusoidal type are used to generate the P-wave. Reflective Neumann (natural) and non-reflective ABC (Absorbing Boundary Condition) boundary conditions based on the non-reflective boundaries of Reynolds (1978) were implemented. The numerical code is written in Fortran 95 language and the Octave graphical interface is used to analyze the results. The GMSH mesher (v. 4.8.4) is used to represent the continuous domain by a set of discrete points that group together form a non-uniform mesh of triangular elements. Numerical tests on square and circular geometries are performed to verify the implementations of the Neumann and ABC boundary conditions. Finally, a good agreement is found between the results of numerical simulations when compared with existing results in the literature.