1D Nonlinear Acoustic Wave Equation In Heterogeneous Fluid

Resumo

In this work, the one-dimensional nonlinear equation of acoustic wave propagation in non-homogeneous fluid was developed using the physical laws of fluid mechanics and thermodynamics for a compressible fluid, including a source term for pressure wave generation. The solution of the 1D Acoustic Wave equation is performed in the time domain using the Petrov-Galerkin Finite Element Method (FEM), and the linear and parabolic approximation basis functions. In wave generation, two different types of pressure source term were implemented, the Ricker type (Chacaltana [1]; Picolli [2]) and the sinusoidal type. The boundary conditions of Neumann (natural reflection) and Reynolds [3] (Absorbing Boundary Condition - ABC) were also implemented and tested. To test the model, a Fortran code was written and a graphical interface in Octave was used to visualize and analyze the numerical results. Simulations were performed in a discrete domain of points representing the one-dimensional mesh. The non-uniform distribution of discrete points was obtained by the GMSH mesh generator. Numerical results were compared with those found in the literature. And, there was a good agreement between them.